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?

The answer is E.

Look at the proposition and read it for what it says: "If the letter is 'E', then the number on the other side is '4'." This is simply saying that if there's an E, then there is a 4, which is basically like saying A is B. You can't jump to conclusions and say that it would logically convert if reversed, because if A is B, B isn't necessarily A. If all squares are quadrilaterals, all quadrilaterals can't be squares. That would make no sense. You'd be ignoring rhombuses and trapezoids and all those other lovely four-sided mathematical shapes. This rules out turning over "4" to verify the proposition. The proposition only says that E is 4, not 4 is E. And, since the proposition only says this, and no other letter or number, then B and 7 have nothing to do with it. So, the answer must be E.

Posted by Sean on 2005-03-06 08:47:21