How can I prove this: $\displaystyle If A \subset B\cup C $ and A and B are disjoint, the $\displaystyle A \subset C. $
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Originally Posted by tigergirl How can I prove this: $\displaystyle If A \subset B\cup C $ and A and B are disjoint, the $\displaystyle A \subset C. $ If $\displaystyle A~\&~B$ are disjoint then $\displaystyle x \in A~ \Rightarrow ~ x\notin B$.
after you answer your question in your other post, this follows directly from that - just write down the definition of disjoint sets, which is that their intersection is the empty set.
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