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

Set Notation - GCSE Maths - Steps, Examples & Worksheet

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

Let A, B and C be sets. Then show that A ∩ (B ∪ C) = (A ∩ B

1.6: Set Operations with Three Sets - Mathematics LibreTexts

Complement (set theory) - Wikipedia

Complement (set theory) - Wikiwand

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

Intersection and union of 3 sets

Set Notation Worksheets, Questions and Revision

Set Notation - GCSE Maths - Steps, Examples & Worksheet