TEST BANK FOR Topology 2nd Edition by James Munkres Converted
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Exam (elaborations) TEST BANK FOR Topology 2nd Edition by James Munkres (Solution Manual)
- Exam (elaborations) • 173 pages • 2021
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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. 
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