I have a maths question suggesting that it is possible to draw a venn diagram where $A \cup C \ne C$ and $A \cup C \ne A$

Question

The question explains it: the question suggests that it is possible, but since union includes everything in both $A$ and $C$, I don't see how it can then not include itself. Thanks for any help you can give me!

Answer 1

Take $A=\{1\}$ and $C=\{2\}$. Then $A\cup C=\{1,2\}$ is not equal to $A$ or $C$. You get $A\cup C=A$ when $C\subseteq A$.