Implications & Contrapositives (1 of 2: How do they relate?)

[ryang]

Hi Eddie, the negation of (P⇒Q) is (P and ¬Q), rather than (P⇒¬Q).

(P⇒Q) and (P⇒¬Q) both have the same truth value when P is false, so they can't be negations of each other.

On the other hand, since the Venn diagrams for (P⇒Q) and (P and ¬Q) are complements of each other, they must be negations of each other.

In particular, the correct negation of your original statement “every prime number has an irrational square root” (true) is “some prime number has a rational square root” (false) instead of “every prime number has a rational square root” (also false).

[jeremypnet]

He’s got the negation of the n is prime implication wrong. There’s an implied “for all” missing from it. The negation is actually “there exists an prime n such that sqrt n is rational.

[patrickwithee]

For anyone wondering: the truth functional conditional has a different negation than the one Mr. Woo presents. However, there is a logic in which the negation he mentions is correct, namely connexive logic. However, I don’t think connexive logic is compatible with contraposition, so I don’t know why he’s using that conditional.

[Prestrev]

A negation is not true, and that doesn’t mean “ opposite” it means there is a gray area ( range of solutions or answers) that can speak to reasons why a negation isn’t true.

[epimaths]

Arithmetic lessons, do you have a lecture on inequality?

[encyclopath]

Are there related definitions for “inverse” and “reverse?”

[nuhd]

Sory im not understand im from indonesia in class 10

[qgame]

If I remember correctly the German word for contrapositive is 'kontraponiert' and I never had a clue where that word came from xD