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

1.6: Set Operations with Three Sets - Mathematics LibreTexts

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

Venn Diagrams and Independence

Complement (set theory) - Wikipedia

Union & Intersection of Sets Cardinal Number of Set

Set Algebra

Draw the Venn diagrams for each of these combinations of the sets

Complement (set theory) - Wikiwand

Solved 3. The symmetric difference of sets, A and B, is