Determine if the following statements are true or false. If true, prove them. If false, find a counterexample. (a) An (B\C) = (A \ B) n (A \ C) (b) If Ac C BC, then A C B. (c) (ANB) UC = (AUC) n(BUC).

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.1: Sets
Problem 10TFE: True or False Label each of the following statements as either true or false. AB=AC implies B=C, for...
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(4) Let A, B, C be subsets of a universal set U.
Determine if the following statements are true or false. If true, prove them. If false, find
a counterexample.
(a) An(B\C) = (A \ B) n (A \ C)
(b) If Ac C BC, then AC B.
(c) (ANB) UC = (AUC) n(BUC).
Transcribed Image Text:(4) Let A, B, C be subsets of a universal set U. Determine if the following statements are true or false. If true, prove them. If false, find a counterexample. (a) An(B\C) = (A \ B) n (A \ C) (b) If Ac C BC, then AC B. (c) (ANB) UC = (AUC) n(BUC).
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