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Forgive my lack of knowledge on this question, but since logically there are many different results in logical connectives, such as exclusive disjunction, what is impossible or not. For an example can logic accept a proposition, where A and B can coexist with Not A and Not B at a single time? There are so much logical tables and diagrams, the Venn diagram for an example, with all possible intersections and so forth, a thought arises, that if proven with consistency, any proposition in logic can be accepted.
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You're reading Reasonably baseless question, but since logic is a study of patterns, what exact patterns are an impossible exception?
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