Logic problem 1 by Dhaval Furia
Four cards are sitting on a table. Each card has an alphabet on one side and an integer on the other.
Two cards are alphabet-side up, and the other two are integer-side up.
These are as below:
Card 1 : A
Card 2 : Z
Card 3 : 2
Card 4 : 9
The statement to be checked is this : for these four cards, if the alphabet-side has a vowel, then the integer-side has an even integer.
What is the maximum number of cards you must turn over to find out whether the statement is true or false?
Bonus: Which cards will you turn over?
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The statement to be checked is p => q, where p : the alphabet-side has a vowel and q : the integer-side has an even integer.
Card 1 satisfies the hypothesis of the statement p => q and hence must be turned over to check whether the statement is true for this card (that is, whether the integer-side has an even integer).
Card 2 doesn't satisfy the hypothesis of the statement p => q and hence it is not necessary to turn over the card in this case.
Card 3 satisfies the conclusion of the statement p => q and hence it is not necessary to turn over the card in this case also (because if the alphabet-side has a vowel then the statement will be true and if it doesn't then we wouldn't care).
Card 4 doesn't satisfy the conclusion of the statement p => q and hence must be turned over to check whether the statement is true for this card (because if the alphabet-side has a vowel then the statement will be false and if it doesn't then we wouldn't care).
So only Cards 1 and 4 must be turned over.
The important thing to realize is that to check whether p => q, it is equivalent to check whether ~q => ~p (and not necessary to check whether q => p)