Let $A$ and $B$ be two sets. If I prove that $a \notin B$ for all $a \in A$, can I say that $A \cap B = \emptyset$?
Are $A$ and $B$ disjoint sets?
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elementary-set-theory
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0Prove by contradiction!!! – 2017-02-19
1 Answers
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Yes. If you prove that $a\in A \Rightarrow a\notin B$, then $A\subseteq B^c$, and that means $$A\cap B \subseteq B^c \cap B =\varnothing$$ so $A\cap B =\varnothing$.
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0Okey, good answer. Thank you very much. – 2017-02-18