Sample Quiz

You have 15 minutes to complete this quiz.

Each of 5 cards has an integer written on one side and a letter written on the other side. The cards are placed on a table so that you can only see one side, and what you see is:

3 A 4 6 B

Which of these cards must be turned over to decide the truth of the statement:
The letter side is a vowel if and only if the number side is odd.

Explain your answer.

Every card must be turned over. In order to verify the statement, you must determine that a vowel is behind the 3, an odd number is behind the A, non-vowels are behind the 4 and 6 and an even number is behind the B. None of these can be deduced, and they are all necessary for the statement to be true. If any of them are false, then the statement is false.