If C is a subset of A and B, then it is a subset of their intersection

by RoRi

June 20, 2015

Prove that if $C \subseteq A$ and $C \subseteq B$ , then $C \subseteq A \cap B$ .

Proof. Let $x$ be any element in $C$ . Then, $x \in A$ since $C \subseteq A$ , and $x \in B$ since $B \subseteq C$ . Therefore, $x \in A \cap B$ . Hence, $C \subseteq A \cap B$ .∎

Stumbling Robot

If C is a subset of A and B, then it is a subset of their intersection

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