Math and Politics

The situation is, people are pissed off at Kerry because he said the following at a rally in Cali:

“You know, education, if you make the most of it, if you study hard and you do your homework, and you make an effort to be smart, uh, you, you can do well. If you don’t, you get stuck in Iraq.”

American soldiers in Iraq, among other groups, were extremely insulted by Kerry's "joke" because it sounded like he was saying that they were dumb.

I just want to say one thing about this whole situation, and it's pretty ironic really because the outcry stems from a logical misinterpretation on the part of the American soldiers: Kerry's statement was not an "if and only if" statement, as we say in the language of math or logic. His statement, broken down into essentials, says

not smart => stuck in Iraq.

American soldiers misinterpreted his statement as:

stuck in Iraq => not smart.

P implies Q doesn't equate to Q implies P, in other words, but it's a mistake we make often in math as students, and in life and politics apparently. I know it's a technicality and probably would annoy people if I tried to point it out, but I just wanted to throw it out there.