Prove that if A and B are subsets of C, then so is their union

by RoRi

June 20, 2015

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

Proof. Let $x$ be any element in $A \cup B$ . Then, by definition of union, we have $x \in A$ or $x \in B$ . If $x \in A$ , then $x \in C$ since $A \subseteq C$ . On the other hand, if $x \in B$ , then $x \in C$ as well since $B \subseteq C$ . Hence, $A \cup B \subseteq C$ .∎

Stumbling Robot

Prove that if A and B are subsets of C, then so is their union

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