There's an explanation at http://pluto.fss.buffalo.edu/classes/psy/segal/416f2001/logic/98logic2.html.

Go to the bottom of the page and check out columns 1,3, and 5. In logic, that "contains" symbol (the sideways U) means "implies" or "if ... then ..."

"If P, then Q" is a proposition that has a value that depends on the values of P and Q. Extracting from that truth table:

P Q P->Q
T T T
T F F
F T T
F F T

The only time P->Q is false is when the premise (antecedent) is true and the conclusion (consequent) is false.

I was kidding a little in my response to Mav - but only a little. I'm not sure that a contradiction can be treated as a false statement. Intuitively it seems that it could, though.

k