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**Possible actuary** This is what I am given: Let A and B be sets. If A or B are not an empty set, then both A and B are nonempty.

I am thinking that this statement is not true and to do a proof by contradiction. But what I came up with does not sound complete.

Assume A or B are not an empty set and either A or B is an empty set. Let x be an element of A. Since A or B are not empty, then B is empty set. Let x be an element of B. Since A or B are not empty then A is empty set. Thus either A or B is an empty set and thus a contradiction.