Smart T-Shirt is Stupid

Yes, I know it's been a while. I've been busy. Stop complaining. I have plenty of things in the pipeline, but no time to get them done.

Anyway, let's get on with this

A certain website is selling this tshirt that has some bogus math on it. Clearly it's intended for people who think they're smart. Quasi-nerds, I suppose.
The tshirt reads:

NO STUDY = FAIL
STUDY = NO FAIL

NO STUDY + STUDY = FAIL + NO FAIL
STUDY (NO + 1) = FAIL (NO + 1)
STUDY = FAIL

Haha. Clever indeed. But this assumes the elements in the equation are commutative. Many things are noncommutative. Subtraction, for instance. Also, matrix multiplication. As we know, STUDY does not equal FAIL. Sure it may once in a while, but not always.

The problem arises in the implied step:
NO STUDY + STUDY = FAIL + NO FAIL
NO STUDY + STUDY = NO FAIL + FAIL
STUDY (NO + 1) = FAIL (NO + 1)

Since STUDY does not equal FAIL, then the implied step can't be done.

So now how about you stop thinking about this and get back to work!