Prove or disprove

For all sets A and B:

If B ⊆ A^c, then A n B = ∅

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- Apr 22nd 2009, 08:55 PMMathWiseNeed some help
Prove or disprove

For all sets A and B:

If B ⊆ A^c, then A n B = ∅ - Apr 22nd 2009, 09:00 PMGammaTrue
suppose not. Then there would be an $\displaystyle x\in B \cap A$. But this means x is in A and x is in B. But since x is in B, and $\displaystyle B \subset A^c$, then x is in the complement of A. But then we have $\displaystyle x\in A^c$ and $\displaystyle x \in A$, which is clearly a contradiction as $\displaystyle A \cap A^c = \emptyset$