Could someone help me out with these set theory proofs? \(A\), \(B\) and \(C\) are sets, and the questions are independent of each other.
Q1. Show that if \(A\subset B\), then \(C-B\subset C-A\).
Q2. If \(P(A)=P(B)\), show that \(A=B\).
Note: \(P(A)\) denotes the power set of \(A\).
Also, could you provide me an faster solution to this question? The question is 'Show that \(A=(A\cup B)\cap(A-B)\)'. My method is to assume that \(a\in A\), and prove that \(a\in (A\cup B)\cap(A-B)\), and hence say that \(A\subseteq(A\cup B)\cap(A-B)\), and prove vice versa. I find this method extremely lengthy. Is there a faster method?