Question

When P is false and Q is true, why is P→Q true?

Answer 1

oh true table for the implies.. yeah that always gets me

Answer 2

Let take a look at the following sentence,
If I get an A, then I'll receive a pizza.

P: I get an A
Q : I'll receive a pizza

Answer 3

P is T
Q is T
P implies Q is T
yes If I do get an A, then I'll receive a pizza

Answer 4

now P is T and Q is F
P implies Q is F
If I get an A, I won't receive a pizza
That's breaking a promise and being unfair.

Answer 5

Suppose P is F and Q is T
If I don't get an A, then I'll receive a Pizza
P implies Q in that situation is T
maybe your parents want to give you the benefit of the doubt and make you happy

Answer 6

Now, P is F and Q is F
meaning If I don't get an A, I won't receive a pizza.
P implies Q is T.
Yeah true...if you're lazy at studying and fail, you don't deserve anything.

Answer 7

If \(P\) is false, then \(P\to Q\) is true regardless of what \(Q\).