9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by showing each is a subset of the other. If not, provide a counterexample. (a) AU A = A. (b) BnB = B. (c) (An B)' = A' B' (d) (A')' = A (e) A\B= (B\A)' (f) (A\B) n(B\A) = 0 (g) If An B=0), then ACB. (h) BxA= A x B. (i) 0× A=0 (i) (A\B) U (B\C) =A\C. (k) (A\B) n(A\C) =A\(BUC)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 87E
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9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by showing
each is a subset of the other. If not, provide a counterexample.
(a) AUA = A.
(b) BnB = B.
(c) (An B)' = A'n B'
(d) (A')' = A
(e) A\B= (B\A)'
(f) (A\B) n(B\A) = 0
(g) If An B = 0), then ACB.
(h) B x A = A x B.
(i) 0× A = 0
(j) (A\B) U (B\C) = A \ C.
(k) (A\B) n (A\C) =A\(BUC)
Transcribed Image Text:9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by showing each is a subset of the other. If not, provide a counterexample. (a) AUA = A. (b) BnB = B. (c) (An B)' = A'n B' (d) (A')' = A (e) A\B= (B\A)' (f) (A\B) n(B\A) = 0 (g) If An B = 0), then ACB. (h) B x A = A x B. (i) 0× A = 0 (j) (A\B) U (B\C) = A \ C. (k) (A\B) n (A\C) =A\(BUC)
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