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

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SOLVED: Prove that for all sets A and B, (A∪B)ᶜ = Aᶜ ∩ Bá

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