I am a Computer Engineering Student. I have watched all your videos and discovered that your videos are the best in the topic. I was really upset seeing no recent uploads. Glad to see you are uploading again. All the Best Bro and keep continuing your work because you are making an Impact.🤗🤗
For conditionals, another logic term that's commonly used when the Proposition is false (the statement that goes with the "If" part) is that we say the Conditional is "Vacuously True". For example, if I have the conditional statement "If I get an A on this exam, then the reason must be that I studied hard", it follows that this statement would be vacuously true if it turns out the proposition is false (the "I get an A" part). To continue the example, if I actually got a different grade like a B on the exam, then the statement is still, oddly, 'vacuously' true since the only way to disprove it would be for me to get an A for a reason other than studying hard (like maybe cheating off of other people!).
Is it equivalent to the "Implication" example that he gave, in which (A --> B) is still "True" when A is false? i.e. (A --> B) is "Vacuously True" when A is False? Edit 1: I think it's applicable in programming too, in the "Else" statement, for example: if (student.grade == 'A') then { print("You have studied hard."); } else { print("You might have studied hard,"); print("but try sleeping more before taking exams."); }
I was having a hard time understanding the logics of implication, the colorful robots helped me a lot to understand the topic completely! I loved the video.
I learnt a lot of those statement overy life, but never thought of 'If and Only If' as being bidirectional. Now that you mentioned it, it looks so obvious!
Is “if and only if” actually bidirectional though? For example: suppose I have a variety of shapes. Some are circles and some are squares. I take some, but not all of the circles and put them in a box. It is true to say “A shape is in the box if and only if it is a circle” but not true to say “a shape is a circle if and only if it is in the box”. In other words, P is the shape being a circle, Q is being in the box. In this case, Q IFF P is true, but P IFF Q is not true. Edit: I have realized my mistake, but I’ll leave this up in case someone else is having the same question. The first condition is not actually “if and only if”. Rather it is simply “only if” The shape is in the box *only if* it is a circle. Which implies that a shape is a circle *if* it is in the box. But it is false to say “the shape is in the box if it is a circle” which means we cannot say “if *and* only if”. We can only say “only if”
Very well explained. I wish my high school teacher had explained the topic like this, using layman terms like "and", "or", "not", "xor", etc. On the other hand, using loads of jargon could make this topic sounds like an extremely complex mathematical equation derived from some black magic.
For a better understanding and simpler/eased calculation logic statements are comparable with venn diagrams and sets like compare negation with complement, conjunction with union and disjunction with interaction and you are good to go.
The content is excellent, but I found a better way to express the 4:50 Implication: If the robot is blue and the blue robot always has an antenna. So when the robot is blue, then it has an antenna.
Hah, yesterday I had this exact subject. I had a hard time understanding equivalence so I looked at the truth table and calculated that it would be equal to ¬P∨Q to help me unferstand how it works, as logic gates are pretty easy to understand. This video helped me understand it clearly. Also pretty much all of this logic can be written as logic gates. Biconditional is just an NXOR, for example.
Not sure if you got a shadowban or something but these videos are 3blue1brown level enjoyable. Me: "yeah. I wonder whats the equivalent of (p exclusive or q)" Answer: " (10 or 01)" Me: 💀
at 1:55 you are wrong: if P = "The robot is blue" then ~P is "It is not the case that the robot is blue". It is a common but silly fallacy to render ~P as Q = "The robot is not blue". Both P and Q imply that the robot exists, but if there is no such robot referenced then P and Q are both false. But of course if P is false then ~P is true, and so clearly ~P != Q.
6:00 What I find interesting, after 30 years of CompSci and 35 years of programming, that (to me) "P implies Q" doesn't at all read as "if P then Q". P -> Q is declarative, whereas I read if P then Q as strictly imperative (if the robot is blue, give it an antenna). If anything, P->Q in code looks like `var implied = P ? Q : true;` or `var implied = !P || Q;` to me, which is still something completely different semantically. I almost never use constructs like this. I feel it's a "may", like you're allowed to eat cake on other days than your own birthday (may as in "legally", vs. "possibly"). That translates to the imperative more directly.
Years ago I wanted to make AI using this logic. I had no idea about neural networks and also I was just a kid lol But this video, even including robots, reminds me of that time. And it's pretty cool.
I got a bit confused in the terms used in the implication part (I am totally lay on this though, maybe it is obvious to others). To me, it is more intuitive to understand it as P->Q being a VALID or in INVALID logical statement in this context, instead of saying it is TRUE or FALSE. Because it being T or F has to do with the particular state of the variables P and Q, which is confusing to me. For example, in the truth table of P->Q, to me P = FALSE makes Q undetermined due to the dependence relation.
No, Third one will be not P, so, False or Q, False False or false is false Last one will be Not P, so, False again or Q, True false or true So it will be true
Bro please make videos on regular basis you tube recommended me this channel and i think this is the most underrated channel,your channel will grow for sure
I only properly understood implication when I saw P -> Q = ¬P \/ Q. Unfortunately, you kind of glossed over why they're equivalent and just showed the truth tables. They're equivalent because P -> Q means "if P is true then Q is also true" and is itself a logical statement which can be true or false. In ¬P \/ Q we see that when P is true ¬P is false so Q must be true to make the whole expression true; if a robot is blue then it must have an antenna otherwise the statement "if a robot is blue it has an antenna" is false. When P is false ¬P is true so Q can be either true or false; if a robot is not blue then it can either have an antenna or not have an antenna, either way it doesn't invalidate the statement that blue robots have antennae because it's not a blue robot. It's also useful to consider ¬P \/ Q in terms of Q, if Q is true then ¬P can be either true or false; if a robot has an antenna then it can be either blue or not blue and if Q is false then ¬P must be true and the robot must not be blue.
thats seems to be quite complicated is there a symbol to represent every combination of your truth table and if so why use extra made up symbols? why not number with like a mark or something 🙃
I am a Computer Engineering Student. I have watched all your videos and discovered that your videos are the best in the topic. I was really upset seeing no recent uploads. Glad to see you are uploading again. All the Best Bro and keep continuing your work because you are making an Impact.🤗🤗
I watched this to learn what the hell a xor is cause im making a mech in gmod with wire mod
I agree, this channel should have 10 million subs. quality is unbelievable.
My professor could not explain it in 50 minutes and you did it in 10. Thank you
This deserves more views! Excellent explanations!
he not upload consistenly enouge
@@toniok.4726 i can see why
The legend is back!
For conditionals, another logic term that's commonly used when the Proposition is false (the statement that goes with the "If" part) is that we say the Conditional is "Vacuously True".
For example, if I have the conditional statement "If I get an A on this exam, then the reason must be that I studied hard", it follows that this statement would be vacuously true if it turns out the proposition is false (the "I get an A" part). To continue the example, if I actually got a different grade like a B on the exam, then the statement is still, oddly, 'vacuously' true since the only way to disprove it would be for me to get an A for a reason other than studying hard (like maybe cheating off of other people!).
Is it equivalent to the "Implication" example that he gave, in which (A --> B) is still "True" when A is false? i.e. (A --> B) is "Vacuously True" when A is False?
Edit 1: I think it's applicable in programming too, in the "Else" statement, for example:
if (student.grade == 'A') then {
print("You have studied hard.");
} else {
print("You might have studied hard,");
print("but try sleeping more before taking exams.");
}
and when the world needed him most, he returned
I was having a hard time understanding the logics of implication, the colorful robots helped me a lot to understand the topic completely! I loved the video.
I thought your voice was familiar and then found out you're Brian Yu from CS50! Very helpful man! keep the work going!
I learnt a lot of those statement overy life, but never thought of 'If and Only If' as being bidirectional. Now that you mentioned it, it looks so obvious!
when its symbol is , it's obvious
my mind was blown when I learned (long time ago) that is "Only If", so they combine into
@@NoNameAtAll2 If only if!
Is “if and only if” actually bidirectional though?
For example: suppose I have a variety of shapes. Some are circles and some are squares. I take some, but not all of the circles and put them in a box. It is true to say “A shape is in the box if and only if it is a circle” but not true to say “a shape is a circle if and only if it is in the box”.
In other words, P is the shape being a circle, Q is being in the box. In this case, Q IFF P is true, but P IFF Q is not true.
Edit: I have realized my mistake, but I’ll leave this up in case someone else is having the same question. The first condition is not actually “if and only if”. Rather it is simply “only if”
The shape is in the box *only if* it is a circle. Which implies that a shape is a circle *if* it is in the box. But it is false to say “the shape is in the box if it is a circle” which means we cannot say “if *and* only if”. We can only say “only if”
@@AlexE5250 The shapes in the box are a subset of the set of circles.
I recognize that voice, CS50 :) I'm glad that finally your channel is taking off!
One of the most underrated channel. Please don’t stop uploading
So easy to understand, you did a good job. This video deserves more views!
Very well explained.
I wish my high school teacher had explained the topic like this, using layman terms like "and", "or", "not", "xor", etc.
On the other hand, using loads of jargon could make this topic sounds like an extremely complex mathematical equation derived from some black magic.
Inb4 this channel absolutely explodes. This is top tier content.
Best introduction on the internet for propositional logic! ❤😊
Please make many more videos!
You’re so underrated. Subbed.
Hope you get to 100k soon!
Damn, when we needed them the most, they showed up. Keep making videos!
I just discovered your channel, best of luck to you, I learned so much watching your videos. And I can say for myself that I am a decent programmer.
For a better understanding and simpler/eased calculation logic statements are comparable with venn diagrams and sets like compare negation with complement, conjunction with union and disjunction with interaction and you are good to go.
Recently came across your channel and I am binge watching. You are a great content creator, please keep it up!
Good content, glad you're back. Keep it up.
Brilliantly explained !!! THANK YOUUUU!!!!!
9:50 I believe this one is an XNOR
I like video of spanking tree they are easy to understand and informational
Can you show us how semaphores and monitors work please ?
With this sublime presentation of yours for sure
thank you brian for such great content! your CS50 intro to django btw is invaluable!
"intro to django" is in which CS50 course??
> _"your CS50 intro to django btw is invaluable!"_
The content is excellent, but I found a better way to express the 4:50 Implication: If the robot is blue and the blue robot always has an antenna. So when the robot is blue, then it has an antenna.
It's always great when you find a precious gem hidden behind the TH-cam algorithm
Hah, yesterday I had this exact subject. I had a hard time understanding equivalence so I looked at the truth table and calculated that it would be equal to ¬P∨Q to help me unferstand how it works, as logic gates are pretty easy to understand. This video helped me understand it clearly.
Also pretty much all of this logic can be written as logic gates. Biconditional is just an NXOR, for example.
not true.
Very Well Explained.
very good video brother👍
... I was so confused. This is a whole lot better than trying to understand my professor...
Not sure if you got a shadowban or something but these videos are 3blue1brown level enjoyable.
Me: "yeah. I wonder whats the equivalent of (p exclusive or q)"
Answer: " (10 or 01)"
Me: 💀
Please never stop creating videos. Take complex data structures and explain it easily. U r too good in that.
Welcome back!
Great video. Love and blessings.
Very good explanation of implication.
Welcome back🤩🤩🤩🤩
at 1:55 you are wrong: if P = "The robot is blue" then ~P is "It is not the case that the robot is blue". It is a common but silly fallacy to render ~P as Q = "The robot is not blue". Both P and Q imply that the robot exists, but if there is no such robot referenced then P and Q are both false. But of course if P is false then ~P is true, and so clearly ~P != Q.
Your content is better than any lecture, wow!
You have a voice of a Ted-Ed instructor. (est un compliment)
HE’S BACK
So is the biconditional the same thing as not xor?
yes
I’m glad you’re back!
Welcome back , Brian !!!
I love how you teach. THANK YOU FOR THIS VIDEO
Thank you!
the exclusive OR is the negation for biconditional
Welcome Back !! Please put a video on Binary Lifting
6:00 What I find interesting, after 30 years of CompSci and 35 years of programming, that (to me) "P implies Q" doesn't at all read as "if P then Q".
P -> Q is declarative, whereas I read if P then Q as strictly imperative (if the robot is blue, give it an antenna).
If anything, P->Q in code looks like `var implied = P ? Q : true;` or `var implied = !P || Q;` to me, which is still something completely different semantically. I almost never use constructs like this.
I feel it's a "may", like you're allowed to eat cake on other days than your own birthday (may as in "legally", vs. "possibly"). That translates to the imperative more directly.
he’s back
Could you do a video on finite state machines?
love your vids, king
welcome back
don't leave us again :(
Thanks alot!
8:44 if we create truth table like Q P Q → P as columns , truth table is same
Please make a video explaining reed solomon error correction its used in data storage like clouds or qr codes i think they are interesting
Happy to see a new upload! Please keep them coming 😃
what I NEEDED!
The goat is back!
Thanks
I'm currently at the knowledge lecture of CS50AI so this was an amazing supplement to the propositional logic topics covered in the course.
I am glad you are back !!! I love your videos
That's Brian... I recognize this voice! :)
please keep uploading videos..
Can you make a video on neural networking?
I love your videos cant wait for the next one
Where have you been dude. Missed you!
Nice video! But you forgot to say that if P -> Q is true, not Q -> not P
Just resubscribed...... Don't stop posting plss!!!
6:09 P->Q = -Q->-P
p xor q is the same as: (p or q) and (not (p and q)),this can be reduced down to:(p or q) and (p nand q),nand is the not of the and of the 2 inputs
Glad to have you back !
6:41
1. Eat the candles
2. Wait a day
3. Eat the cake
Years ago I wanted to make AI using this logic. I had no idea about neural networks and also I was just a kid lol
But this video, even including robots, reminds me of that time. And it's pretty cool.
do an intro to linear logic or HoTT
bro just takes a 2 year break, then comes back without an apology even, props to you.
Your back!!
What about his back?
I need to known logic connectivity ❤
thanks teachar
I got a bit confused in the terms used in the implication part (I am totally lay on this though, maybe it is obvious to others). To me, it is more intuitive to understand it as P->Q being a VALID or in INVALID logical statement in this context, instead of saying it is TRUE or FALSE. Because it being T or F has to do with the particular state of the variables P and Q, which is confusing to me.
For example, in the truth table of P->Q, to me P = FALSE makes Q undetermined due to the dependence relation.
Please please don't stop making videos
Well explained!
Love your videos but the audio could use some post processing to take out the high ends. Good stuff tho!
7:40 But in the case of the not p or q all except the last should be true?
No,
Third one will be not P, so, False or Q, False
False or false is false
Last one will be
Not P, so, False again or Q, True
false or true
So it will be true
Next vid when
This reminds me of an old movie named, "If This Is Tuesday Then We Must Be In Belgium." The logic of comedy?
Two years and two months!
(p -> q) (not q -> not p)
Bro please make videos on regular basis you tube recommended me this channel and i think this is the most underrated channel,your channel will grow for sure
❤️
This better used in electronics than coding
This is amazing.
great
I only properly understood implication when I saw P -> Q = ¬P \/ Q. Unfortunately, you kind of glossed over why they're equivalent and just showed the truth tables.
They're equivalent because P -> Q means "if P is true then Q is also true" and is itself a logical statement which can be true or false. In ¬P \/ Q we see that when P is true ¬P is false so Q must be true to make the whole expression true; if a robot is blue then it must have an antenna otherwise the statement "if a robot is blue it has an antenna" is false.
When P is false ¬P is true so Q can be either true or false; if a robot is not blue then it can either have an antenna or not have an antenna, either way it doesn't invalidate the statement that blue robots have antennae because it's not a blue robot.
It's also useful to consider ¬P \/ Q in terms of Q, if Q is true then ¬P can be either true or false; if a robot has an antenna then it can be either blue or not blue and if Q is false then ¬P must be true and the robot must not be blue.
wooo! i love this explanation!
Exclusive OR>>> "either"
I knew I recognized that voice!
thats seems to be quite complicated is there a symbol to represent every combination of your truth table and if so why use extra made up symbols? why not number with like a mark or something 🙃