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

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.∎

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