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h/t to Larry - Moe and Curly (and maybe others) for catching this. (STOLLEN / MODUS TOLLENS)
The argument in the meme is INCORRECT.
It says that if P is false, then Q is false. Not so.
The correct logic says that if Q is false, then P is also false.
Example:
P = it is sunny.
Q = I go to the beach.
(If P, then Q.) If it is sunny I go to the beach.
(If Q is false, then P is also false.) This means that it is true that if I did not go to the beach, then it was not sunny.
It is NOT (necessarily true) that if it is not sunny I did not go to the beach. Because the original statement says nothing about what I might do if it is not sunny. Perhaps on some non-sunny days I go to the beach on on some I don’t. It only asserts that I’m for sure at the beach if it’s sunny.