Conditional Statements: if p then q
ฝัง
- เผยแพร่เมื่อ 16 พ.ค. 2017
- Learning Objectives:
1) Interpret sentences as being conditional statements
2) Write the truth table for a conditional in its implication form
3) Use truth tables to see the disjunctive form of a conditional statement as logically equivalent
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This video was created by Dr. Trefor Bazett
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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.
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.
🥰😍
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.
This is mirrored, are you really left handed!!!
Your Voice guides me
'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 😅
Is he writing the words backwords so that we can read them? If so this guy deserves a Nobel prize.
same broo😭😭😭
Using this to study for the LSAT. Thanks for the video, helps a lot!
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.
finally i got the explanation that i want, ur smart and the way u explan is very clear ...thanks a lot
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.
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.
I’m teaching truth tables to my students and this video is great!
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:)
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
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.
Thank you for helping my college algebra course make more sense. You rule.
Thank you so much, really appreciate that!
you just save my life !
i started to learn computer science last month, and your teaching give me a purpose !
That was super helpful! Your teaching was clear and easy to understand. Thank You!
Hey Dr. Trefor, you are amazing! Thanks for sharing it.
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.
Really great , I was really confused before watching ur video. Now my concept is crystal clear. Love u dude.
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 👍
Sir this is so helpful... It really helped me.
this vid has been given to me by the online teacher cuz the quarantine
Is this considered a tautology
Took me a few stop and starts, reviewing and writing but when it clicked... amazing thank you!
this just made my day like i understand this easily so grateful to you for that
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
7:08 mins worth it :) Thank you so much, Dr. Trefor Bazett
Well this was amazing.
It starts to make sense.
Thank You very much!
Thanks, that was really helpful
This is helpful.. now u r a part of my JEE journey ❤❤
Fantastic explanation, thank you
I'm currently going through your playlist and this is really helping me study for my midterm. Thanks!
Best of luck!
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!
very good explanation. This is what i were looking for!
Really thanks. It's crystal clear now.
Thank you so much, I couldn't interpret that the statement was based if p was True in all scenarios of the conditional statement.
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".
Tysm! It helped me a lott! God bless you!
Thanks, very clear and succinct
Boom, you got a new sub.
Thank you!
I'm learning from you not only the information but the skill of delivering the information. Thank you for your efforts.
My pleasure!
Thank you sir, this makes sense a lot!!
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
Thank you for your amazing explanation
thanks a lot trefor bazett i understood the concept very clearly
Dude, you had me by 4:30 explaining how conditionals arrive at whether they are true or not.
Fantastic video. Just finish a chapter on implications and found your video.
How do you think about if q then p?
You saved me so much time studying. Everything just clicked.
Thanks for the simple video dude.
much better explained than my professor, thanks :)
Great explanation.
Very good explanation. I am reading Discrete Maths by Kenneth and was little confused by the explanation there.
It's fun to learn when Marc Gasol is the one teaching you
Lol. I also noticed that
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!
so after you make this chart how do you read it to make a conclusion from it?
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.
Amazing explantation sir...
This Is An Instant TH-cam Classic!
A million thanks for the explanation
Thank you!
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 you!!
Very well explained, maintained lecture quality like a Senior Professor.
I m inspired by your tremendous way of delivering lecture. Stay blessed
Thank god there's teachers in youtube
I replayed the last 20s until I understood them, about four times that is. Now I understand, thanks man
You are doing Gods work.
Thank You Marc Gasol!
Thank you.
Pls I need more of this, how can I get the series pls?
thank you very much. I have finals this week
I want things on if statements.
Nice video
Thanks a lot
Nice explanation
Great job 💕 appreciate it alot
You have done it all🙏
amazing explanation thanks
Thank You!
I wasnt able to wrap my head around why the bottom two rows were interpreted as True until I saw this video, thank you
Awesome explanation
This one gets everyone, every time.
This was really helpful, but still left me with questions on problems such as “~rv(~p->q)”
Thank you Sir...
Is this marc gasol? Thanks for the help.
Hmm.. Starting to make sense
Thank you sir ,it helped ...
I'd like to hear some examples.
This is what u used in pC repair use statements in fixing PC cause or effect
thank you
thank you so much
Thank you !! Helped me a lot in my finals 😢
thanks big dawg
great explanation
thank you sir
Satisfied, thx