Problem 2h. Munkres Topology Section 1.1 Confirmation

Question

I'm learning (or trying to) topology from Munkres' Topology. I believe I've solved 2h in Section 1.1, but I wanted to confirm with someone that I am doing it right. Here it is:

$ A\cup (B - C) = (A \cup B) - (A \cup C)$

I believe that this is false, and here's why. On the RHS, you have elements in $A \cap C$ that you don't have on the LHS. Therefore, I believe that there is a backwards implication ( $\impliedby$). Can someone confirm or tell me where my logic is wrong? Thank you so much :)

Answer 1

Let $A = \{1, 2, 3\}$, $B=\{3, 4, 5\}$ and $C=\varnothing$. Then $2 \notin (A\cup B) - (A \cup C)$ yet $2 \in A \cup (B-C)$. So, I'm inclined to believe you are right (if you've interpreted the problem correctly).