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?

You must turn over 7 and E. 

"If X, then Y" is false if X is true and Y is false. It is true for all other conditions. X="card has E" and Y="card has 4". 

X is true, Y is false if and only if some card with E has a number other than 4 on the other side. 

If 7 has an E on the other side, or if E has a number other than 4 on the other side, the hypothesis is disproved. Otherwise it is proved for the 4 card deck.      

I originally said you had to turn over 4. I realized that was incorrect after reading Nikki's post.

If 4 has an E on the other side, that is "X is true, Y is true." Irrelevant.

If 4 has a T on the other side, that is "X is false, Y is true." Irrelevant.

If B has a 4 on the other side, that is "X is false, Y is true". Irrelevant.

If B has a 2 on the other side, that is "X is false, Y is false". Irrelevant.

 

 

Edited on December 15, 2004, 3:32 pm

Posted by Penny on 2004-12-15 15:14:04