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

SOLVED: Draw the Venn diagrams for each of these combinations of

Complement (set theory) - Wikipedia

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

Intersection and union of 3 sets

Union (set theory) - Wikipedia

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

Venn Diagram - GCSE Maths - Steps, Examples & Worksheet

Answer the following four (4) questions based on the information