Prove the Following Statement Using an Element Argument and Reasoning $\text { For all sets } A , B \text {, and } C , ( A \cup B ) \cap C \subseteq A \cup ( B \cap C ) \text {. }$

Essay

Prove the following statement using an element argument and reasoning directly from the
definitions of union, intersection, set difference. $\text { For all sets } A , B \text {, and } C , ( A \cup B ) \cap C \subseteq A \cup ( B \cap C ) \text {. }$