I present to you a deck of 4 cards. Each card has on one side a letter of the alphabet, and on the other side a single digit from 0-9.

I propose a hypothesis that may apply to this deck:
If the letter is 'E', then the number on the other side is '4'.

I then drop the 4 cards on the table, and you see: 'B', '7', 'E', '4' (on the respective cards).

Which of the 4 cards must you turn over to verify or disprove my hypothesis?

First, turn over the 'E' to see if there's a '4'. If it's not, the hypo is disproved. But if there is a '4' on the other side, that does not prove the hypo, b/c there may be an 'E' on the other side of the '7' card, which would disprove the hypo. So you have to turn that card over, too. If there's an 'E', the hypo is disproved. You don't need to turn over the '4' card, b/c even if a letter other than 'E' is there, it doesn't disprove the hypo (hypo states "If 'E', the '4', so 'E' MUST give '4', but a letter other than 'E' can give '4' as well). You don't have to turn over the 'B', b/c the hypo is silent about what 'B' would have on the other side--it could be any digit, including '4'.

Posted by mick on 2004-12-19 03:58:29