False Implies True is...

[Theraot]

This is how you conceptualize this:

{A => B} <=> (A, B) do not contradict inferring B from A. Understand inferring B from A that knowing A is true is enough to know B is true, however A being true might not be necessary for B being true.

If and only if A is true and B is false, we would have found a situation where inferring B from A does not work. Meaning that we found evidence that the inference rule from A to B is wrong.

If we find that A is false and B is true, that does not contradict inferring B from A. It just confirms that A being true is not necessary for B being true.

[mayipalma]

No entendí nada de lo que dijiste (del idioma) pero sí pude comprender lo demás. Ojalá mi profesor de Álgebra hubiera explicado las cosas así cuando vimos lógica.

[Theraot]

If the policy is that when you get into an accident you get money... That does not tell you what happens when you do no get into an accident. You may get money, you may not. One would conclude it is undefined. You do it with a syllogism. You can deduce that you get money from the policy and the accident, but you cannot deduce that you get money from the policy and lack of accident. If doing knowledge representation, that's what I'd do.

Edit: see inference rules and formal language.

[Jubf]

This video is out in the perfect timing
I just saw a question using F implies T for prove in today math lesson and I was confused
Thx for the video

[drewpatterson]

I see, so on my next exam I should put my answers in the form p implies q and then put a wrong answer for p so I am guaranteed to get 100% correct!

[ulvc]

Why does this video is unlisted? Am I the only one who watched it? I'm special!!!

[nomoremathhere]

I used to write T for all the T/F problems. Then I would wait for the teacher to go over the answers, then all I needed to do is to add a - to T so it would look like F. Unfortunately I could only do that on worksheets not exams.

[alanhiguera]

another way to see why f=>t and f=>f should be true is by motivation of the if and only if statement (iff). iff should hold true when both premises are the same truth value and iff should be false if p and q differ in truth value. p iff q is defined as p=>q and q=>p. if f=>t or f=>f were to be false, then iff would not work as we understand it to be.

[thedoublehelix]

We learned about this in my computer science class. Logic is a lot of fun!

[ai_serf]

my problem with this video, is that he's not discussing the logic behind implication, i.e. modus ponens, necessity and sufficiency. he's just putting in math expressions and evaluating the truth value.
the true importance and power of p->q is that it helps us describe the world ( if it's raining then i'll get wet), and helps us formalize logical entailment. implication is the one foundational concepts in building all of mathematics through logical entailment. it's pretty insane.

[michel_dutch]

How about a vid on the NOR (or NAND) operator, the only operator you'll ever need. 😋

[MrRyanroberson]

Have you considered proving the law of non-contradiction? That it is necessarily false that statements (generally) are allowed to contradict

[TrackopGaming]

Nice video, Dr. Peyam. Could you please upload more of these basic logic-related videos?

[epicmorphism]

Love you so much! Thank‘s for all your interesting videos!

[theproofessayist]

"Most feared statement" - pulls up Epsilon Delta definition of a limit. HAHAHAHHAHA!!! Good one Dr. Peyam. If you're up to it, a video on nested predicate quantifiers would be greatly appreciated. Thank you for explaining the truth table of the conditional through analogies. My math professor never bothered to correct the counter-intuition we naively have with F->T and just expected us to rote memorize it from textbook. Concentration was only spent on doing the exercises. Thank you for your service. Oh and just for encouragement for fellow mathematicians don't worry if you still don't completely get or like logic - there are mathematicians that hate studying logic too. It's a free country!

[sudheerthunga]

Hey Dr.Peyam! I am kinda new to this channel...could you tell me some of the best videos of yours...
P.S. A sophomore.

[joelpaddock]

Whenever I've been stuck with implication (every time), I either remind myself "Ex falso quodlibet" or I remember that if the truth table wasn't this way it would be some other logic relation like bi-implication.

[carlosvargas]

Justamente estoy viendo un capítulo de introducción a la topología y este tipo de temas me dejan pensando

[rataleprosa]

it is true that something false can imply something true. This word "can" admits that there is another possible case, namely, F implies F.

[majciak]

Hi dr Peyam! Would you mind to do a separate series or at least a video about tensors and its applications in calculus and differential geometry? I've always wanted to get to know this branch of mathematics, but unfortunately tensors weren't part of my linear algebra course and (at least for me) It's really hard to understand the core idea of it. Btw in my opinion your channel is the best youtube channel about math. Greetings from Poland!