Prove some more relations between sets

by RoRi

June 20, 2015

Prove that $A \subseteq A \cup B$ and that $A \cap B \subseteq A$ .

Proof. If $x$ is any element of $A$ , then by definition of $A \cup B$ , we have $x \in A \cup B$ (since $A \cup B$ is the set of elements in either $A$ or $B$ ). Thus, $A \subseteq A \cup B$ . ∎

Proof. If $x$ is any element of $A \cap B$ , then $x \in A$ since $A \cap B$ is defined to be the set of elements that are in both $A$ and $B$ . Therefore, $A \cap B \subseteq A$ . ∎

Stumbling Robot

Prove some more relations between sets

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