Problem: I tell you that if a card has a vowel on one side, then it has an odd number on the other side. Right now, you see symbols E, S, 3, and 8 on the sides that are up. So, what are the minimum amount of cards you must check to verify the statement is true?
Teacher's Answer: Let P = "the card has a vowel", Q = "the card has an odd number on one side"
We lift the vowel E, because if it's false, the statement P --> Q is false.
We don't lift S, because if the statement P --> Q is true, Q can be true regardless of P.
We don't lift 3, because again, Q can be true regardless of P.
We lift 8, because according to the statement not Q --> not P, P --> Q is false if the card has a vowel.
My question: The statement P --> Q is equivalent to "not P or Q". So, can we verify the original statement is true by knowing that S is not a vowel (equivalent to not P), and 3 is an odd number (equivalent to Q)? This way, you could verify the statement with just 1 card instead of 2?