elementary set theory - $(A\cap B)\cup C = A \cap (B\cup C)$ if

I have a set identity: $(A \cap B) \cup C = A \cap (B \cup C)$ if and only if $C \subset A$. I started with Venn diagrams and here is the result: It is evident that set identity is correct. So I

Union & Intersection of Sets Cardinal Number of Set

The ( left( A cap B ^ { prime } right) ^ { prime } cup ( B cap C

Complement (set theory) - Wikiwand

If [math]A, B[/math] and [math]C[/math] are three sets, how to

Prove `A cup (B cap C)=(A cup B) cap(A cup C)`

Principle of Inclusion and Exclusion (PIE)

DM4CS Methods of Proof for Sets