You are presented with the four cards shown below, and told that each card has a

number on one side, and a

letter on the other.

`
----- ----- ----- -----
| | | | | | | |
| 2 | | 7 | | J | | R |
| | | | | | | |
----- ----- ----- -----
`

You are told to determine which cards must be turned over in order to test the

validity of the following statement:

*If a card has a J on one side, then it must have a 7 on the other side*
This will serve as a sort of buffer paragraph to prevent you from inadvertently cheating. It is highly recommended that you actually take the two seconds and figure out which cards you would turn over. This particular test is a third- or fourth-generation derivative of Peter Wason's original test of logical reasoning, which was devised in 1966, but the structure and analysis are identical (well, not my analysis below, but the way in which the answers you choose partially indicate your capacity for logic).

And now, you will find out what your answers say about you:

**If you chose to turn over the J**, consider yourself a literate English speaker. That is, just about anyone with a basic understanding of English will get this answer right. From a logical standpoint, you recognize that the statement *If P then Q* is violated if P is true but Q is false.

**If you chose to turn over the R**, then you either (a) read the question wrong, (b) mistrust the experimenter (i.e., you think that there's a possibility that the statement *each card has a number on one side and a letter on the other* was a lie or trick (which it was not)), or (c) think that the statement *If P then Q* can be proven false under some condition in which P is not true. Unfortunately, if (c) is the case, you have next to no capacity for logical reasoning.

**If you chose to turn over the 7**, then you, like many people, made the erroneous assumption that if a J is not on the other side of the 7, then the statement would be false. The statement made no condition for cards with 7's on them, only J's. If the card has a J on the back, the statement is true. If the card does not have a J on the back, the statement still holds. Still confused? See the truth table for implication below.

**If you chose to turn over the 2** then consider yourself as being in at least the 90th percentile (might be higher, I don't remember the actual numbers) for this test. Maybe you're very clever, or maybe you've taken an introductory course in philosophy or mathematical analysis. In any case, you recognized that on the back of the 2 there had to be a letter besides J in order for the statement to be true: *If not-Q, then not-P*, which is the contrapositive, and thus the logical equivalent of *If P then Q*.

If that was all too convoluted and you just wanted the answers, they were J and 2. Why, you ask? I already explained! But I'll explain again by way of the following truth table for implications:

`
P | Q | P => Q
----------------
T | T | T
T | F | F
F | T | T
F | F | T
`