Lemma 5.13. Let A be a subset of a universal set U. Then: (1) AUA = U. (2) An Ac = 0. Hence, A and Aº partition U. Exercise 5.8. Prove Lemma 5.13 Do not use the De Morgan laws, which will be discussed below.

Lemma 5.13. Let A be a subset of a universal set U. Then: (1) AUA = U. (2) An Ac = 0. Hence, A and Aº partition U. Exercise 5.8. Prove Lemma 5.13 Do not use the De Morgan laws, which will be discussed below.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.4: Prime Factors And Greatest Common Divisor

Problem 25E: Prove that if m0 and (a,b) exists, then (ma,mb)=m(a,b).

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Lemma 5.13. Let A be a subset of a universal set U. Then:
(1) AUA
=
U.
(2) An Ac = 0.
Hence, A and Aº partition U.
Exercise 5.8. Prove Lemma 5.13 Do not use the De Morgan laws, which will be
discussed below.

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