My thought process for this have always been: -If I guessed RIGHT then answered RIGHT, it make sense(it is RIGHT) -If I guessed RIGHT then answered WRONG, it doesn't make sense (it is WRONG) -If I guessed WRONG then answered RIGHT, it still make sense (It is RIGHT) -If I guessed WRONG then answered WRONG, it still make sense (It is RIGHT) Basically if you guessed Right in the first place, there's no reason for you to answer wrong, otherwise it will make the whole statement wrong(doesn't make sense). But if you guessed wrong in the first place, you cannot assume your answer will be right or wrong. So either way, any kind of conclusion will make the statement right (make sense)
I thought if p and q as a promise I promise that: if p happens then q will happen too if p happens -> q happens : True (promise is upheld) if p happens -> NOT(q happens) : False (promise is broken) if NOT(p happens) -> q happens : True (promise is upheld) if NOT(p happens) -> NOT(q happens) : True (promise is upheld) example: I promise that: if you have a dog then it is blue have dog -> color is blue : True have dog -> color is not blue : False have cat -> color is blue : True (original promise about dogs being blue is still True) have cat -> color is red : True (cats being red doesn't affect my promise) just because you have a cat doesn't mean my promise is broken. cause my promise is about DOGS being blue. cats got nothing to do with it.
If I study Hard -- then I will pass == Satisfied with result :) If I study Hard -- then I don't pass == not satisfied with result :( If I don't study hard -- then I pass == F**k Yeah I am satisfied :D I I don't study hard -- then I don't pass == F**k it, I didn't study so I am satisfied with results :) I hope this made better sense, these TH-cam videos makes it more complicated sometimes :D
This was incredibly helpful. My textbook feels so incredibly over-saturated with unnecessary information and it was overwhelming. The simplicity here and your clear explanation saved my grade this week! Thank you so much!
What I found ungrateful, is that without the textbook, you wouldn't have come here in the first place to understand. Let's honor the textbook for being (sometimes) way too dense.
'Vacuous truths' - brilliant! Truth tables were easy right up to the p(false) implies q (true) line, and this has really stumped me. Other videos just say 'memorise the outputs' and failed to explain WHY the outputs were the way they are for conditional statements - memorising was easy but this video really helped me understand the underlying logic - thank you!
@@badwrong you’re correct that the term “visual learner” isn’t actually a real learning “style”. That being said, I still found the visual format of this video helpful for my comprehension on this subject matter. Take care :)
@@Juan-yj2nn yes it does its kinda hard to explain but p implies q means: First: if p is true, q must be true (p=true IMPLIES that q=true) Second: if p isn't true, p IMPLIES q is also true, no matter what q is. (Think about it: if p isnt true, it's still true that a case where p is true, q is also true) Now what is true in any case here, if p-->q is true? If we look at both rules we find that the statement is always true when q is true or when p is false This gives ~p v q Now is this a coincidence or re they logically the same in any way? Well.. using human language to describe logic is difficult because human language is vague. The words we use to describe logic (if p then q / p implies q / p AND q etc) are ways to emulate the meaning of logic to human language. If the logic is the same, it's the same, in real life, anywhere. It means the same, it is the same in any way same or form. The thing that's different is our emulation of the logic. The word AND, is the closest we'll get to the real "logical meaning". The best way to emulate in human language/think about p --> q in my opinion is like this: --> is a logical operator that evaluates the truth value of a **promise of a theory leading to a conclusion** , where p is the hypothesis and q is the conclusion. Might sound difficult but if to bring it a little closer to human language: think of it like a scientist that promises you that if p is true, then q is true. Whether his promise is held or not determines the truth value . So if p=true leads to q being true, he doesn't break the the promise. If p=true leads to q being false, he breaks his promise: his theory didnt lead to the right conclusion. If p=false (his theory doesnt work) his entire promise isn't broken. It's the PROMISE (and the promise and all the logic, in whatever way you interpret that, what represents the logic of -->). For the promise to hold, the hypothesis being true what makes the conclusion being true a necessity For the promise to hold, the conclusion being false is what makes the hypothesis being false a necessity This is the relation of --> In logic terms: For p--> q to be true: p being true, REQUIRES q to be true (it won't hold when q is false) q being false REQUIRES p to be false (it wont hold if p is true) Hmmm.. so the logic is based on 2 requirements for two situations and all other situations are true it seems. (Just like how the logic of AND is based on 1 requirement: p and q need to be true at the same time) The 2 requirements, things that need to be true at least are: p being false or q being true In other words: ~p v q
You're videos are going to be my savior in my discrete mathematics class. My professor is extremely confusing when she's trying to explain pretty much everything. The textbook helped, but there were still some things I needed some clarification on and you explained them perfectly. Thank you so much for taking the time to make these videos.
I was so stumped when I read this in my textbook, I'm prepping for my upcoming math class and want to understand the concepts before class starts. This was VERY helpful! Subscribed!
I'm currently studying this for university entrance exam here in Mexico, so I came across this chanel. Your explanation is definitely easier than my textbook but I was still confused with some parts of the video so I will have to watch it as many times as needed to get it all. Thanks for the content.
Thank you, I finally got it looking this and other your videos! I had to develop a bit more resonating with myself explanation though. Hope it will help somebody more as well. :) Say, my (actually yours from another video :)) implication is: If it is a dog, then it is a mammal. Then, my implication is considering a dog (being a mammal) only, not a cat or a table. I agree (It is true) that when it is not a dog (p = false), then it can be anything -- mammal or not mammal (q is true or false). Thus, my implication is TRUE in both cases when it is not a dog -- then everything is all right with my implication, and I AGREE that (not a dog) can be anything. But when it is a dog, then my implication is ONLY TRUE when it is a mammal -- because it is what I specifically imply! Otherwise, my implication is FALSE. I.e. when it is a dog, and it is not a mammal -- then and only then my implication FAILS. Only then my implication is WRONG. CONCLUSION: Implication is FALSE ONLY when it is WRONG! Let's create a new boolean result: WRONG! :))
"if p, then q" example is "if it is a dog (p), then it is blue (q)." This is logically equivalent to "it is either NOT a dog (p) OR it is blue (q)". It kind of makes sense if I think of it like this...
Thank you so much for this video Dr. Bazett!! I had been spinning my wheels on this Critical Thinking module for the past six hours when I came across this video. Super helpful!! You're definitely getting a sub from me!
You gave me a complete idea and you opened my logic! THANK YOU FOR THIS VIDEO! I needed this , because they taught us this in university, but i didnt understand!!! but now I do! The way you teach is wonderfulllll! thanks again! Greeetings from Turkmenistan
Cool! So in essence, you cannot derive a false conclusion from a true assumption. I'm so glad I found this channel. The way you break down and explain concepts reminds me of a former Math teacher that first sparked my interest in Algebra.
I'm just here because my girlfriend was teaching me this early and I want to take interest in the things she enjoy.. great video now let me go make her happy
I have an Intuitive explanation. My statement is: “Whenever I wear a blue jacket then I wear black shoes”. So, in the first row, this statement is true. But in the third row, it is also true, because I didn't say, that I wear black shoes only when I wear a blue jacket but that when I wear a blue jacket I wear black shoes (my point is that black shoes are not a condition for anything, I can wear black shoes with whatever I want, but when I wear a blue jacket then I must wear black shoes, so “blue jacket” is a condition that implies black shoes, and not another way around. This means that I can wear a white jacket and black shoes but the statement:” Whenever I wear a blue jacket then I wear black shoes” doesn't have anything to do with this, it is still true that always when I wear a blue jacket than I must wear black shoes. So this implication is not true only when I do something contradictory to what I claim, for example, I say that: “Whenever I wear a blue jacket then I wear black shoes” and then instead I take some other shoes, for example, I wear a blue jacket but I take some red Nike ✔️. Similarly is for the 4th row. But 2nd the row is the only one that is in contradiction with my statement or claim.
I’m studying philosophy right now, which is how I came across your video, but this makes so much sense for understanding Stats since I took it last year. My memory is foggy, but this video helps!
Thank goodness for this video, I nearly cried trying to do my geometry homework with no knowledge of what a conventional statement was because my geometry teacher didn't explain what those where to anyone in the class.
Dude is very helpful and easy to understand as you teaching visually and we can able understand easily thank you so much and hats off to you for teaching brilliantly.
Thank you so much! When you put the definition there with the type of statement you listed early on, it helped me SO much. One book I'm trying to read for class is not the most organized for this sort of thing.
Hi Trefor, thanks for this video. Quite a few books that I referred to skip the last two cases completely or gloss over it without going into even a minimal depth. I see you dint skirt the last two cases and in fact your study/pass example put things in better context. I'm taking Logic as a subject in a course on Philosophy and can see where this trouble originates. It lies in the epistemology of different philosophies. The classical Western/Aristotelian ( multi valued logic addresses this gap ) version of truth is True/False , 0/1. However classical /ancient Indian philosophy has a layered or more nuanced version of truth. 7 versions, actually, ranging from True to False! Some of the indeterminate ones are - somehow ( or sometimes) true, somehow ( or sometimes ) untrue, Both true and false ( think Both sides claiming victory in a war!), Neither true nor false.....etc. This layered approach to truth is reality of life and where all confusions, conflicts, distrust, outrage arise. When life is black & white, this works perfectly, but breaks down when things are grey. In short, the real answer to the 2 cases when P is "F" should be "unknown".
im a programmer and i was getting really frustrated because this should be a walk in the park for me and I wasn't getting it but turns out It's just an issue of it not "translating" to a language i understand. Really helped when you explained it like hypothesis and conclusion because then I was able to figure out what it means and "translate" it
One example that I find helpful for understanding this: p: "It is raining." q: "The ground is wet." p -> q: "If it is raining, then the ground is wet." - If it is indeed raining (p = true), and if the gorund is indeed wet (q = true), then my argument (p -> q) is RIGHT (p -> q = TRUE). - If it is indeed raining (p = true), but the ground is NOT wet (q = false), then my argument (p -> q) is WRONG (p -> q = FALSE). This is because it contradicts the claim that rain causes the ground to be wet. - If it isn't raining (p = false), then regardless of the condition of the ground (if it's wet or not), my argument remains RIGHT (p -> q = TRUE). This is because if the condition (rain) doesn't occur, the statement can't be proven false. Since we can't prove the falsity of the statement, it remains true. I like to think of this as: "Innocent (true) until proven guilty (false)."
the biconditional ones had confused a lot. I thought of this example which made a lot of sense to me. If your friend can fly by himself in the sky then you can too. The truth value of it is true
I think this will help the most: "If p then q" isnt the same as "If and only if p, then q". "If p then q", only means that when p is true, then q should aswell be true. But it can also happen that p was not the case, but q still be true. We havent discard that possibility, we have just said that, "if p happends to be true, then q is true aswell", but we havent said, "only if p is true, then and only then q can be true aswell".
My logic says that they are more vacuously false than true, especially for F=>T=T (I can think about F=>F=F more or less logically, but not about F=>T=T). To me, this does not look like logic but as a purely volitional decision to accept it as true, while it is neither true nor false. And I can't move on until I get it.
My thought process for this have always been a hypothesis arriving to a conclusion (p-->q) -If I guessed RIGHT then answered RIGHT, it make sense(it is RIGHT) -If I guessed RIGHT then answered WRONG, it doesn't make sense (it is WRONG) -If I guessed WRONG then answered RIGHT, it still make sense (It is RIGHT) -If I guessed WRONG then answered WRONG, it still make sense (It is RIGHT) Basically if you guessed Right in the first place, there's no reason for you to answer wrong, otherwise it will make the whole statement wrong(doesn't make sense). But if you guessed wrong in the first place, you cannot assume your answer will be right or wrong. So either way, any kind of conclusion will make the statement right (make sense)
My thought process for this have always been:
-If I guessed RIGHT then answered RIGHT, it make sense(it is RIGHT)
-If I guessed RIGHT then answered WRONG, it doesn't make sense (it is WRONG)
-If I guessed WRONG then answered RIGHT, it still make sense (It is RIGHT)
-If I guessed WRONG then answered WRONG, it still make sense (It is RIGHT)
Basically if you guessed Right in the first place, there's no reason for you to answer wrong, otherwise it will make the whole statement wrong(doesn't make sense). But if you guessed wrong in the first place, you cannot assume your answer will be right or wrong. So either way, any kind of conclusion will make the statement right (make sense)
omg this is so helpful, i learn faster this wayyy
wow , you are brilliant, thanks
WOW, You are a genius. Thanks for this so much!
I thought if p and q as a promise
I promise that:
if p happens then q will happen too
if p happens -> q happens : True (promise is upheld)
if p happens -> NOT(q happens) : False (promise is broken)
if NOT(p happens) -> q happens : True (promise is upheld)
if NOT(p happens) -> NOT(q happens) : True (promise is upheld)
example:
I promise that:
if you have a dog then it is blue
have dog -> color is blue : True
have dog -> color is not blue : False
have cat -> color is blue : True (original promise about dogs being blue is still True)
have cat -> color is red : True (cats being red doesn't affect my promise)
just because you have a cat doesn't mean my promise is broken. cause my promise is about DOGS being blue. cats got nothing to do with it.
🥰😍
If I study Hard -- then I will pass == Satisfied with result :)
If I study Hard -- then I don't pass == not satisfied with result :(
If I don't study hard -- then I pass == F**k Yeah I am satisfied :D
I I don't study hard -- then I don't pass == F**k it, I didn't study so I am satisfied with results :)
I hope this made better sense, these TH-cam videos makes it more complicated sometimes :D
you are a fucking legend. You helped me so much i was strugling to remember the if then table now i will not forget it. Thanks my g
i knew something like this was similiar to domain and range fungtion. except the x variable where change to Truth varioable.
Helpful🔥
Seems like not studying makes us satisfied anyway
Thanks, now I remember.
Bless my professor literally rushed through this entire topic in two sentences, gotta hate summer classes
Likewise it's been a challenge for me finite maths
😢gdgxsfcl❤ggd🎉hdmvl@@marciahuell
Hvzlr
This was incredibly helpful. My textbook feels so incredibly over-saturated with unnecessary information and it was overwhelming. The simplicity here and your clear explanation saved my grade this week! Thank you so much!
Glad it was helpful!
@@DrTrefor 9
My textbook is written by someone who just wanted to fill the book with words without going through the trouble of explaining things
What I found ungrateful, is that without the textbook, you wouldn't have come here in the first place to understand.
Let's honor the textbook for being (sometimes) way too dense.
Thank you for helping my college algebra course make more sense. You rule.
Thank you so much, really appreciate that!
'Vacuous truths' - brilliant! Truth tables were easy right up to the p(false) implies q (true) line, and this has really stumped me. Other videos just say 'memorise the outputs' and failed to explain WHY the outputs were the way they are for conditional statements - memorising was easy but this video really helped me understand the underlying logic - thank you!
Dude this was so helpful- I'm a visual learner and this is just brilliantly done
No such thing as a "visual learner"...
@@badwrong veritasium
@@badwrong you’re correct that the term “visual learner” isn’t actually a real learning “style”. That being said, I still found the visual format of this video helpful for my comprehension on this subject matter. Take care :)
@@badwrong If there's no such thing "visual learner," then define it in a new way such that it exists.
@@badwrong Not true 😅 Pun intended 😅
I love a teacher who is enthusiastic and teaches at an understandable speed. Such a good combo. It's so common you only get one of the two.
Explaining it using the ~p V q logical equivalency really helped me to finally grasp implication. Thanks!
How is that ~p V q has nothing to do with real life implication?
@@Juan-yj2nn yes it does its kinda hard to explain but p implies q means:
First: if p is true, q must be true (p=true IMPLIES that q=true)
Second: if p isn't true, p IMPLIES q is also true, no matter what q is. (Think about it: if p isnt true, it's still true that a case where p is true, q is also true)
Now what is true in any case here, if p-->q is true? If we look at both rules we find that the statement is always true when q is true or when p is false
This gives ~p v q
Now is this a coincidence or re they logically the same in any way? Well.. using human language to describe logic is difficult because human language is vague. The words we use to describe logic (if p then q / p implies q / p AND q etc) are ways to emulate the meaning of logic to human language. If the logic is the same, it's the same, in real life, anywhere. It means the same, it is the same in any way same or form. The thing that's different is our emulation of the logic.
The word AND, is the closest we'll get to the real "logical meaning".
The best way to emulate in human language/think about p --> q in my opinion is like this:
--> is a logical operator that evaluates the truth value of a **promise of a theory leading to a conclusion** , where p is the hypothesis and q is the conclusion. Might sound difficult but if to bring it a little closer to human language: think of it like a scientist that promises you that if p is true, then q is true. Whether his promise is held or not determines the truth value . So if p=true leads to q being true, he doesn't break the the promise. If p=true leads to q being false, he breaks his promise: his theory didnt lead to the right conclusion. If p=false (his theory doesnt work) his entire promise isn't broken. It's the PROMISE (and the promise and all the logic, in whatever way you interpret that, what represents the logic of -->).
For the promise to hold, the hypothesis being true what makes the conclusion being true a necessity
For the promise to hold, the conclusion being false is what makes the hypothesis being false a necessity
This is the relation of -->
In logic terms:
For p--> q to be true:
p being true, REQUIRES q to be true
(it won't hold when q is false)
q being false REQUIRES p to be false
(it wont hold if p is true)
Hmmm.. so the logic is based on 2 requirements for two situations and all other situations are true it seems.
(Just like how the logic of AND is based on 1 requirement: p and q need to be true at the same time)
The 2 requirements, things that need to be true at least are: p being false or q being true
In other words: ~p v q
This is mirrored, are you really left handed!!!
Your Voice guides me
You're videos are going to be my savior in my discrete mathematics class. My professor is extremely confusing when she's trying to explain pretty much everything. The textbook helped, but there were still some things I needed some clarification on and you explained them perfectly. Thank you so much for taking the time to make these videos.
Using this to study for the LSAT. Thanks for the video, helps a lot!
I was so stumped when I read this in my textbook, I'm prepping for my upcoming math class and want to understand the concepts before class starts. This was VERY helpful! Subscribed!
Really glad it helped, good luck in your class:)
I'm currently studying this for university entrance exam here in Mexico, so I came across this chanel. Your explanation is definitely easier than my textbook but I was still confused with some parts of the video so I will have to watch it as many times as needed to get it all. Thanks for the content.
finally i got the explanation that i want, ur smart and the way u explan is very clear ...thanks a lot
7:08 mins worth it :) Thank you so much, Dr. Trefor Bazett
I’m teaching truth tables to my students and this video is great!
Thank you, I finally got it looking this and other your videos!
I had to develop a bit more resonating with myself explanation though.
Hope it will help somebody more as well. :)
Say, my (actually yours from another video :)) implication is:
If it is a dog, then it is a mammal.
Then, my implication is considering a dog (being a mammal) only, not a cat or a table.
I agree (It is true) that when it is not a dog (p = false), then it can be anything -- mammal or not mammal (q is true or false).
Thus, my implication is TRUE in both cases when it is not a dog -- then everything is all right with my implication, and I AGREE that (not a dog) can be anything.
But when it is a dog, then my implication is ONLY TRUE when it is a mammal -- because it is what I specifically imply!
Otherwise, my implication is FALSE. I.e. when it is a dog, and it is not a mammal -- then and only then my implication FAILS.
Only then my implication is WRONG.
CONCLUSION: Implication is FALSE ONLY when it is WRONG!
Let's create a new boolean result: WRONG! :))
loved this explanation
"if p, then q" example is "if it is a dog (p), then it is blue (q)." This is logically equivalent to "it is either NOT a dog (p) OR it is blue (q)". It kind of makes sense if I think of it like this...
Thank you so much for this video Dr. Bazett!! I had been spinning my wheels on this Critical Thinking module for the past six hours when I came across this video. Super helpful!!
You're definitely getting a sub from me!
You're very welcome!
Really great , I was really confused before watching ur video. Now my concept is crystal clear. Love u dude.
You gave me a complete idea and you opened my logic! THANK YOU FOR THIS VIDEO! I needed this , because they taught us this in university, but i didnt understand!!! but now I do! The way you teach is wonderfulllll! thanks again! Greeetings from Turkmenistan
You're so welcome!
you just save my life !
i started to learn computer science last month, and your teaching give me a purpose !
Thank you So Much Sir 🙌. Your Video Helped me Understand the very thing I was having a doubt in.
This one was Precise and Short 👍
this vid has been given to me by the online teacher cuz the quarantine
Is this considered a tautology
Thank you for explaining the scenarios where the initial statement is false :)
Cool! So in essence, you cannot derive a false conclusion from a true assumption.
I'm so glad I found this channel. The way you break down and explain concepts reminds me of a former Math teacher that first sparked my interest in Algebra.
Wow Good class. Thanks very much
I'm learning from you not only the information but the skill of delivering the information. Thank you for your efforts.
My pleasure!
This helped me so much. Thank you, your truly saving many students
Hey Dr. Trefor, you are amazing! Thanks for sharing it.
I'm just here because my girlfriend was teaching me this early and I want to take interest in the things she enjoy.. great video now let me go make her happy
this just made my day like i understand this easily so grateful to you for that
Sir this is so helpful... It really helped me.
I'm currently going through your playlist and this is really helping me study for my midterm. Thanks!
Best of luck!
I have an Intuitive explanation. My statement is: “Whenever I wear a blue jacket then I wear black shoes”. So, in the first row, this statement is true. But in the third row, it is also true, because I didn't say, that I wear black shoes only when I wear a blue jacket but that when I wear a blue jacket I wear black shoes (my point is that black shoes are not a condition for anything, I can wear black shoes with whatever I want, but when I wear a blue jacket then I must wear black shoes, so “blue jacket” is a condition that implies black shoes, and not another way around. This means that I can wear a white jacket and black shoes but the statement:” Whenever I wear a blue jacket then I wear black shoes” doesn't have anything to do with this, it is still true that always when I wear a blue jacket than I must wear black shoes. So this implication is not true only when I do something contradictory to what I claim, for example, I say that: “Whenever I wear a blue jacket then I wear black shoes” and then instead I take some other shoes, for example, I wear a blue jacket but I take some red Nike ✔️. Similarly is for the 4th row. But 2nd the row is the only one that is in contradiction with my statement or claim.
Mind-blowing 🎉❤
This is helpful.. now u r a part of my JEE journey ❤❤
Very well explained, maintained lecture quality like a Senior Professor.
I m inspired by your tremendous way of delivering lecture. Stay blessed
Incredible 😁 love from India sir❤
I’m studying philosophy right now, which is how I came across your video, but this makes so much sense for understanding Stats since I took it last year. My memory is foggy, but this video helps!
Thank goodness for this video, I nearly cried trying to do my geometry homework with no knowledge of what a conventional statement was because my geometry teacher didn't explain what those where to anyone in the class.
You saved me so much time studying. Everything just clicked.
much better explained than my professor, thanks :)
That was super helpful! Your teaching was clear and easy to understand. Thank You!
Dude is very helpful and easy to understand as you teaching visually and we can able understand easily thank you so much and hats off to you for teaching brilliantly.
how he is writing
This is why i like literature more😭😭😭😭
This Is An Instant TH-cam Classic!
You are doing Gods work.
Thank you so much sir for this great enlightenment ❤
Thank you so much! When you put the definition there with the type of statement you listed early on, it helped me SO much. One book I'm trying to read for class is not the most organized for this sort of thing.
Tysm! It helped me a lott! God bless you!
How do you think about if q then p?
It's fun to learn when Marc Gasol is the one teaching you
Lol. I also noticed that
Fantastic video. Just finish a chapter on implications and found your video.
Very good explanation. I am reading Discrete Maths by Kenneth and was little confused by the explanation there.
Thank god there's teachers in youtube
Great explanation.
thank you very much. I have finals this week
very good explanation. This is what i were looking for!
I replayed the last 20s until I understood them, about four times that is. Now I understand, thanks man
Thank you !! Helped me a lot in my finals 😢
Thanks for the simple video dude.
Hi Trefor, thanks for this video. Quite a few books that I referred to skip the last two cases completely or gloss over it without going into even a minimal depth. I see you dint skirt the last two cases and in fact your study/pass example put things in better context.
I'm taking Logic as a subject in a course on Philosophy and can see where this trouble originates. It lies in the epistemology of different philosophies. The classical Western/Aristotelian ( multi valued logic addresses this gap ) version of truth is True/False , 0/1. However classical /ancient Indian philosophy has a layered or more nuanced version of truth. 7 versions, actually, ranging from True to False! Some of the indeterminate ones are - somehow ( or sometimes) true, somehow ( or sometimes ) untrue, Both true and false ( think Both sides claiming victory in a war!), Neither true nor false.....etc. This layered approach to truth is reality of life and where all confusions, conflicts, distrust, outrage arise. When life is black & white, this works perfectly, but breaks down when things are grey. In short, the real answer to the 2 cases when P is "F" should be "unknown".
Thank you so much, I couldn't interpret that the statement was based if p was True in all scenarios of the conditional statement.
Well this was amazing.
It starts to make sense.
Thank You very much!
im a programmer and i was getting really frustrated because this should be a walk in the park for me and I wasn't getting it but turns out It's just an issue of it not "translating" to a language i understand. Really helped when you explained it like hypothesis and conclusion because then I was able to figure out what it means and "translate" it
One example that I find helpful for understanding this:
p: "It is raining."
q: "The ground is wet."
p -> q: "If it is raining, then the ground is wet."
- If it is indeed raining (p = true), and if the gorund is indeed wet (q = true), then my argument (p -> q) is RIGHT (p -> q = TRUE).
- If it is indeed raining (p = true), but the ground is NOT wet (q = false), then my argument (p -> q) is WRONG (p -> q = FALSE). This is because it contradicts the claim that rain causes the ground to be wet.
- If it isn't raining (p = false), then regardless of the condition of the ground (if it's wet or not), my argument remains RIGHT (p -> q = TRUE). This is because if the condition (rain) doesn't occur, the statement can't be proven false. Since we can't prove the falsity of the statement, it remains true.
I like to think of this as: "Innocent (true) until proven guilty (false)."
This was really helpful, but still left me with questions on problems such as “~rv(~p->q)”
Took me a few stop and starts, reviewing and writing but when it clicked... amazing thank you!
Thank You Marc Gasol!
Hello I am from india this question is in my text book your teaching was easily understanding thank you
underrated video
You have done it all🙏
I want things on if statements.
Nice video
OMG tank u very much. I already knew theories but I wanted to know really wats going on in under two rows. I think i got it 😁👍
Dude, you had me by 4:30 explaining how conditionals arrive at whether they are true or not.
Thanks, that was really helpful
This one gets everyone, every time.
thanks a lot trefor bazett i understood the concept very clearly
Awesome explanation
Really thanks. It's crystal clear now.
so after you make this chart how do you read it to make a conclusion from it?
Thank you sir ,it helped ...
I wasnt able to wrap my head around why the bottom two rows were interpreted as True until I saw this video, thank you
the biconditional ones had confused a lot.
I thought of this example which made a lot of sense to me.
If your friend can fly by himself in the sky then you can too.
The truth value of it is true
Fantastic explanation, thank you
Thanks, very clear and succinct
Thank you sir, this makes sense a lot!!
thank you sir
this is it. This is the video you've been looking for to explain this. Look no further-what you need is right here.
God bless u sir ❤
Thank you!!
I think this will help the most:
"If p then q" isnt the same as "If and only if p, then q".
"If p then q", only means that when p is true, then q should aswell be true.
But it can also happen that p was not the case, but q still be true.
We havent discard that possibility, we have just said that, "if p happends to be true, then q is true aswell",
but we havent said, "only if p is true, then and only then q can be true aswell".
Ohmagaaaa
My logic says that they are more vacuously false than true, especially for F=>T=T (I can think about F=>F=F more or less logically, but not about F=>T=T). To me, this does not look like logic but as a purely volitional decision to accept it as true, while it is neither true nor false. And I can't move on until I get it.
My thought process for this have always been a hypothesis arriving to a conclusion (p-->q)
-If I guessed RIGHT then answered RIGHT, it make sense(it is RIGHT)
-If I guessed RIGHT then answered WRONG, it doesn't make sense (it is WRONG)
-If I guessed WRONG then answered RIGHT, it still make sense (It is RIGHT)
-If I guessed WRONG then answered WRONG, it still make sense (It is RIGHT)
Basically if you guessed Right in the first place, there's no reason for you to answer wrong, otherwise it will make the whole statement wrong(doesn't make sense). But if you guessed wrong in the first place, you cannot assume your answer will be right or wrong. So either way, any kind of conclusion will make the statement right (make sense)
Amazing explantation sir...
So that means IF I don’t study hard THEN I will pass the test anyway?
Actually it's the ~
great explanation
Thanks sir for exampling god bless you sir