The symmetric difference of set A and B, denoted by A∆B, is the set containing elements in eitherA or B, but not in both A and B. Answer the followings: (a) Let A = {a, e, f, y, q, w} and B = {e, z, z, q,p, f}. Find AAB.(b) Draw Venn Diagram of (AUB) – (AnB) and (A-B)U(B-A). Conclude that AAB = (AUB)- (ANB)and AAB=(A - B)U(B-A).(c) Using set identities and part (b) show that AAB = (ANB)n (AUB).

(a) Let A = {a, e, f, y, q, w} and B = {e, x, z, q,p, f}. Find AAB. (b) Draw Venn Diagram of (AUB) – (AnB) and (A-B)U(B-A). Conclude that AAB = (AUB) - (ANB) and AAB=(A - B)U (BA). (c) Using set identities and part (b) show that AAB = (ANB) n(AUB).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 16E

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Question

The symmetric difference of set A and B, denoted by A∆B, is the set containing elements in either
A or B, but not in both A and B. Answer the followings:

(a) Let A = {a, e, f, y, q, w} and B = {e, z, z, q,p, f}. Find AAB.
(b) Draw Venn Diagram of (AUB) – (AnB) and (A-B)U(B-A). Conclude that AAB = (AUB)- (ANB)
and AAB=(A - B)U(B-A).
(c) Using set identities and part (b) show that AAB = (ANB)n (AUB).

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