How to subset proof

Question

I don't understand how to prove subsets of a universe by induction. I have only just started learning sets.

 Let B, C be subsets of a universe U.

 Prove that C' - B' = B - C

Thank you, any examples would be highly appreciated.

Answer 1

Note \begin{align*} x\in C'-B'&\iff x\in C'\cap x\not\in B'\\ &\iff x\not\in C\cap x\in B\\ &\iff x\in B-C. \end{align*}