Truth and falsehood can overlap. In other words, that contradictions can be true. The reason for this is paradoxes like the liar's paradox. The sentence, "this sentence is false," is both true and false at the same time in the same sense. Building on that, mathematics made the wrong choice philosophically when they modified the axioms of set theory instead of changing the logic in which it was embedded and keeping naive comprehension and extensionality. @asklemmy