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?

(In reply to 3 Scenarios by Syzygy)

"If numbers are unique but duplication is permitted... then turn over either 'E' or '4'"

I disagree.  Turning over the 4 won't verify or disprove SK's hypothesis.  That would be using the converse, which is never a valid arguement (don't feel bad, I've accidentally used it too).  Just because If A then B is true, If B then A is not necessarily true.  We could find an X on the other side of the 4, and it would not disprove the hypothesis.

At first I only thought about turning over the E, but then I saw O³'s post and agree with him about turning over the 7 and the E.  Here's why.  First, simply using If A then B... since we see a card with an E on it, the other side must be 4 in order for the hypothesis to be verified, and if it is some other number then it is disproven.

Using the contrapositive, If not B then not A, we see a card with a 7 on it (which is not 4).  If we see "not E" on the other side, then the hypothesis is verified, and if we do see an E, then it is disproven.

The B card could have anything on the other side (including a 4) and that doesn't mean anything.  The 4 could have anything on the other side (including an E) and that wouldn't mean anything either.

Posted by nikki on 2004-12-15 13:58:47