Q1 Plz solve both parts kindly plz take your time and get a thumb up plz 1.Prove that for all sets A and B and n E Z, n ≥ 1, the following holds:(a)72(=1nU(A\B) = (UA) \ B;i=171(b) n(AB) = (n A) \ B.(=1i=1 1.Prove that for all sets A and B and n EZ, n ≥ 1, the following holds:11n(a) U(A¡ \B) = (U A ¡ ) \ B ;i = 1i = 111n(b) n(A¡ \B) = (^ A ¡ ) \ B .i=12

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Answered: Prove that for all sets A and B and…

Prove that for all sets A and B and nEZ, n ≥ 1, the following holds: 72 11 (a) U(A\B) = (UA) \ B; (=1 i=1 n n (b) n(AB) = (n A) \ B. i=1 i=1

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.2: Properties Of Group Elements

Problem 31E: 31. Prove statement of Theorem : for all integers and .

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Q1 Plz solve both parts kindly plz take your time and get a thumb up plz

1.
Prove that for all sets A and B and n E Z, n ≥ 1, the following holds:
(a)
72
(=1
n
U(A\B) = (UA) \ B;
i=1
71
(b) n(AB) = (n A) \ B.
(=1
i=1

1.
Prove that for all sets A and B and n EZ, n ≥ 1, the following holds:
11
n
(a) U(A¡ \B) = (U A ¡ ) \ B ;
i = 1
i = 1
11
n
(b) n(A¡ \B) = (^ A ¡ ) \ B .
i=1
2

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