TEST BANK FOR Topology 2nd Edition by James Munkres Converted

Chapter 1 Set Theory and Logic x1 Fundamental Concepts Exercise 1.1 Check the distributive laws for [ and and DeMorgan's laws. Solution: Suppose that A, B, and C are sets. First we show that A (B [ C) = (A B) [ (A C). Proof. We show this as a series of logical equivalences: x 2 A (B [ C) , x 2 A ^ x 2 B [ C , x 2 A ^ (x 2 B _ x 2 C) , (x 2 A ^ x 2 B) _ (x 2 A ^ x 2 C) , x 2 A B _ x 2 A C , x 2 (A B) [ (A C) ; which of course shows the desired result. Next...