Find three sets $A$, $B$, $C$, each of them non-empty, such that $(A\cap B)\cup C=A\cap(B\cup C)$ and $(A\cap B)\cup C\neq A\cap(B\cup C)$ I need to find three sets for both statements I have above. I have tried drawing Venn diagrams and shading appropriately then adding numbers in each shaded region to try and guess and check for sets $A$, $B$ and $C$ but am unsure how to find an appropriate solution.

$$B \subset C \subset A$$
$$A \subset B \subset C$$
For general view is good to write right hand side as:
$$(A\cap B)\cup C=(A \cap B) \cup(A \cap C)$$
now you see, that difference between sides is difference between sets from right hand of union: on left you have $C$ on right $(A \cap C)$ and on this way you can create any example you would like.
