Conditional Statements

We look at the notion of conditional and biconditional statements along with an example of a compound statement.

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[goodplacetostop]

15:00

Weirdly enough, when I had my first lessons in logic classes at university, I had a better understanding of implication using ¬P ∨ Q instead of P→Q, especially the case False → False "equals" True.

Anyway that Logic series brings me a lot of memories. Ok, that’s a good place to stop.

[victorrizkallah]

Keep going with the logic videos they're great. Good job

[perappelgren]

As always - relaxed, down to earth and crystal clear. Great work!

[RolandThePaladin]

The second biconditional statement is false. Consider f(x) = x^3. Then f'(0) = 0, but f has no local extreme at x = 0.

[miserepoignee]

8:20 Is this actually a biconditional statement? f'(x) = 0 could occur at an inflection point that is not a local extremum, no?

[masterjopots]

Let's support his channel by not skipping the ads.

[AeroCraftAviation]

11:00 I am slightly confused by this. It states that the falsity of (P and Q) equals the falsity of P or the falsity of Q. Because of the "or" these are mutually exclusive and exhaustive of the total solutions. But there exists a third solution: not(P) + not(Q). If both were individually false, they would also be compositely false, and therefore not(P and Q) = not(p) + not(Q) . Is this correct?

[dhwyll]

Typo (chalko?) at 7:40: "if and only if" rather than "if and if."

[Justuy]

need of the hour!!! Even my Math teacher writes that thing in the thumbnail wrong :'(

[CrikoDarkness]

If we negate the "exclusive or" table will be equivalent to "biconditional" table,
i want to see this in your next logical video ♡♡♡

[ldbspg]

Is this the same as material implication? It seems to be equivalent to logical consequence considering in the examples the truth of a statement depends on whether or not a statement logically follows from another. However the truth table is the same as material implication...

[snniper]

Distributive rule of OR operation over AND operation is it P v (Q^R)=(P v Q)^(P v R) ?

[antoniussugianto]

Prof Penn do you teach complex tetration?

[DeanCalhoun]

based michael with the green new deal shirt!!

[nadonadia]

proof the truth of this mathematical statemant

(if you were my math teacher when i was in college) then (i would have done math for the rest of my life)
Here we have P the Q always truth.

[Andreyy]

Hmm pretty interesting... So basically if we define some axioms(statements) as terminals, and define logicals, if, etc. as transitions, we would achieve a grammar, whose L(G) would be all the theorems. If so it's provable that in general it's undecidable to know if a theorem t is in L(G), or with other words that theorem is true for axiom base. A truly rough idea, but sounds interesting to investigate.

[nathanisbored]

could you also say something like "P mutually implies Q" as another way to say P iff Q?

[TrueBagPipeRock]

u should get cash app. ppl would tip a few bux