SOLUTION: Let S and T be sets. Prove that if x ∉ S ∩ T, then X ∉ S or X ∉ T.

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Question 644513: Let S and T be sets. Prove that if x ∉ S ∩ T, then X ∉ S or X ∉ T.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If x ∉ S ∩ T, then x is NOT in both sets at the same time. So it must be in one or the other set (or in neither set). So x is exclusively in one set, but not in the other.

So say x is in set T, but not in set S. Then X ∉ S would be true.

OR

say x is in set S, but not in set T. Then X ∉ T would be true.

If x is in neither set, then both X ∉ S and X ∉ T would be true.