Card Play

Logic Level 2

The following cards each have an integer on one side and are colored either red or blue on the other:

Claim: If a card has an even number on one side, then the other side is red.

Which two cards do we have to turn over to show that the claim is true?

red and blue card 8 and blue card 8 and red card 11 and red card 11 and blue card

2 solutions

Vishwash Kumar Γξω
Nov 21, 2016

He has to know whether an even numbered card is red or not.

It doesn't matter what color the 11 card has, since it will not disprove the claim that "an even numbered card is red".
It doesn't matter what number the red card has, since it will not disprove the claim that "an even numbered card is red".

He needs to turn over card number 8 to ensure that it is red,
and to turn over the blue card to ensure that it does not have an even number on it.

Thus, the 2 cards are "8 and blue card".

Simply turning over 8 and the blue card does not ensure anything. What if by chance 8 is red and blue is even. Nothing is proven. That is simply a 25% probability. Two instances does not prove the claim it only allows the claim to persist. It is still possible for the red card to have an odd integer

Mark Brown - 2 years, 11 months ago

Oliver Boorman
Nov 20, 2016

We can test this claim using the transposition rule that states $A \implies B$ if and only if NOT B $\implies$ NOT A.

If we turn over the '8' card and the back is red, the claim holds for the positive case. If it is blue, the claim is disproved. By the transposition rule, we also need to turn over the blue card and check that has an odd number of the front. If it does, we have proved the claim, otherwise again the claim is disproved.

do you mean not B --> not A?

William Nathanael Supriadi - 4 years, 6 months ago

Thanks! I've edited the solution to reflec that.

Calvin Lin Staff - 4 years, 6 months ago

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