Most people think the answer is card A and card C. However, the correct answer is that you need to check card A and card D.
Whether there is a vowel or a consonant on the other side of card C makes no difference. The statement "every card with a vowel on one side has an even number on its opposite side" can only be shown to be false if there is an odd number on the opposite site of card A and/or a vowel on the opposite side of card D.
In his book Finding Moonshine Professor Marcus Du Sautoy offers the following explanation for why most people get the answer to this puzzle wrong: "Our brains are so desperate for symmetry that they also check wehther every card with an even number on one side has a vowel on the other. So the brain directs you to pick up card C. ... It seems that our subconscious works according to some sort of symmetrical logic. It thinks that if the statement 'if A then B' is true, then so is its converse, the mirror image, 'If B then A'. In general, this is far from true. Logical deduction is usually very unsymmetrical."
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