$A$,$B$,$C$, are subsets of a set $S$. Prove the following set identity using the laws of set theory (set identities)
$\left(A\cup C\right)\cap[\left(A\cap B\right)\cup\left(C'\cap B\right)]=A\cap B$
I'm not exactly sure how to use the identities to solve this problem, and I'm having trouble understanding how to properly apply the identities. Can you guys help guide me in solving this problem?