I Contradict You!

Logic Level 2

There are five two-sided cards lying on a table. Each card contains a letter on one side and a positive integer on the other. Two cards show the letters $A$ and $B$ . The other three cards show the numbers $2, 4, 6$ . The back sides of these cards are not visible.

Alice says, "If a card has an odd number on one side, then the other side must have a vowel."

Bob proved Alice wrong by turning over one card. Which card is it?

A 2 4 B 6

2 solutions

Steven Yuan
May 9, 2015

Alice's statement is logically equivalent to its contrapositive:

"If a card does not have a vowel on one side, then it does not have an odd number on the other."

Bob needs to show that there is a card with a consonant on one side and an odd number on the other, thereby contradicting Alice's statement. Thus, Bob must have turned over the card with the letter $\boxed{B}$ .

After the answer was revealed I thought back to the title and was quite the disappointment :D

William Garcia - 5 years, 5 months ago

Guilherme Monteiro
Jul 13, 2015

Alice claims that if a card has an odd number on one side, it must have a vowel on the other, however, she does not imply that if a card has a vowel on one side it will, necessarily, have an odd number on the other.

Therefore, cards 2, 4 and 6 could have vowels on their backs an that would mean nothing, just as card A could have an even number on its back and still mean nothing.

Card B, however, if revealed to present an odd number on its back, would disprove Alice's statement, thus making it the only one worth turning over.

I Contradict You!

2 solutions

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