Logic 101 (#9): Conditional (If-Then) Statements

This lecture introduces the IF-THEN logical operator, commonly also known as the conditional, material conditional, or implication. If the first half of a conditional is true, then the second half of the conditional must be true as well.

Unlike other logical connectors, conditionals appear in English in many different formats. This lecture looks at a few of the more common ones: "only if," "required," "sufficient," and "necessary."

[anthonyaportela]

I wanna see if I can clear some confusion. Some people are confused that this statement is not reversible. The statement can be edited to be reversible if you change "only if" to "if AND only if".


For example: "(You can play video games) IF AND ONLY IF (you've finished your homework)" is a reversible statement. This is because it secretly holds several statements in one. "if AND only if" combines the forward version of a statement with it's backward version.


SO! If you have "(You can play video games) IF (you've finished your homework)", you have V->H.
If you have "(You can play video games) ONLY IF (you've finished your homework)", you have H->V.
BUT! if you have "(You can play video games) IF AND ONLY IF (you've finished your homework)", you have the conjunction of both;
(V->H)^(H->V) which is the same as saying V<->H.


Hope I could help someone. It definitely helped me typing it down.

[janreskovac]

I was a bit confused by the examples, until you pointed out the difference between antecedent and consequent. Then it all made sense. Great video(s).

[juliehadley]

I honestly wish I had found your videos sooner. You make things easier to understand. Thank you!

[ohad]

This is the first day of my master's econ studies. You saved me in my bachelor's, and you will save me once again. Thank you.

[bradleyli]

Hope more people have the chance to view the series of videos on logic! Thanks man! Its so helpful!!

[hckr_-ghse]

I got all of these wrong until the end of the video, and then it all clicked, thanks man!

[xopowo]

You are very logical! You are my favorite teacher ever!
Thank you!

[ayastein]

+William Spaniel But Sir, In Example 2, both the statement and the converse are true
If you can play video games, than you must've done your HW
so V=>H
and if you did your HW, then you can play video games
V holds and H holds too, we express it with the notation V<=>H
In the statement V, we're talking about the possibility of playing video games, it'll only be possible if you did your HW, but you don't actually have to play video games, but it's still true that it's possible if you'd done your HW
Please correct me if I'm wrong

[agentmikster]

The only one that got me confused was #2.
Are they not reversible?
1. If you have finished your homework, you can play video games. (Because wouldn't finishing your homework automatically allow you to play video games, even if you don't?)
2. You can only play video games if your homework is finished.

So to me it seems like V <=> H

Although I don't think it would work if you take out the "Can".

[Merione]

Ex #1: P->(O^C) [right]
Ex #2: H->V [wrong]
Ex #3: T->L [wrong again]
Ex #4: M->(~F) [wrong again]
Ex #5: F->U [right, I redeemed myself]

[Glendragon]

Great video, but could explain why it doesn't go the other way, like how License -> Driver test, but not Driver Test -> license, because you can pass the driving test and still not get it for failing vision test or have it rewoked.

[pulkiitsharma]

why cant we write this as " he maintains a 1000 dollar balance this implies he does not pay a negation fee."

[PunmasterSTP]

Conditional? More like "conduit to wonderful" knowledge; thanks for all these amazing videos!

[mohammadtogar]

This is my attempt at answering each examples:

Example 1: P ^ O v C
Example 2: H = V
Example 3: T = L
Example 4: M = F
Example 5: F = U

I guess I got most of them wrong except for the last one. I still keep on switching each of them up.

[ratdood]

Ex1: P => (O . C)
Ex2: V => H
Ex3: L => T
Ex4: ~F => M
Ex5: U => F

[LydiaOnYT]

1. P => (O^C)
2. H => V
3. T => L
4. ~M => F
5. F => U

I rock at this.

[TheYahmez]

GOT IT.
Just because you've finished your homework doesn't mean the electricity is running and the internet works.
But if nothing's stopping you then that includes the homework, which must therefore be 'done' or rendered moot by the dog, which could be considered 'done' in a manner of speaking but i digress.

[AndyHoke]

Just because the antecedent is false, it does not necessarily follow that the consequence is also false. I'll demonstrate this if anyone doubts this.

[osmio]

Example #1: P=>(O^C) // got it right!

Example #2: I think both "If you've finished your homework, then you can play video games." and "If you can play video games, then you've finished your homework." could work. Maybe both H=>V and V=>H are valid so it's some kind of reciprocal condition? Such as (H=>V)^(V=>H). // aaand I was wrong.

Example #3: "If one has a driver's license, the one passed the test" maybe? So L=>T // correct!

Example #4: "If one doesn't want to pay absurd bank fees, then it is necessary for one to mantain a $1, 000 balance". I'm guessing the first statement has to be considered as a negative version of "one wants to pay absurd bank fees"; my answer is ~F=>M // correct =D.

Example #5: "If one has finished Game Theory 101, then one has a basic understanding of game theory". I'll go ahead and answer F=>U // I was right!

[jaceking]

I really dont get the statement at the end that

P -> Q = -P v Q

Looking at example 5 for instance, if finishing game theory 101-> understand game theory

This implies that one does not finish game theory OR they understand game theory??

What if they underatand game theory from an alternative means? Or what about if someone did finish game theory 101 but didnt underatand it. Does all of my confusion have to do witb the first proposition not being true itself?