I don't think of logic that way. Logical statements are true by definition within any particular system of logic, regardless of what the universe looks like. Same for math.

Consider the difference between Euclidean and non-Euclidean geometry. Is one true and the other false? The question makes no sense. But one is more useful under certain conditions (short distances on Earth or any other planet) and the other under different conditions (long distances on Earth or between planets).