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2. For each statement, Determine if it is True. If it is true then prove it. If it is False then disprove it or prove its negation. (a) For all n e Z?, if n is composite, then there exists an integer d such that d\n and 1 < d < vd. (b) There exists a pair of integers x and y such that 8x + 14y = 1. (c) For all positive integers a, b, c if a|c and b|c then ab|c. (d) For all sets A, B,C, if AUC CBUC then A C B. (e) For all sets A, B, if A C B then BC A. (f) For all sets A, B, if A Ç B then (AU B) – (An B) # 0.

2. For each statement, Determine if it is True. If it is true then prove it. If it is False then disprove it or prove its negation. (a) For all n e Z?, if n is composite, then there exists an integer d such that d\n and 1 < d < vd. (b) There exists a pair of integers x and y such that 8x + 14y = 1. (c) For all positive integers a, b, c if a|c and b|c then ab|c. (d) For all sets A, B,C, if AUC CBUC then A C B. (e) For all sets A, B, if A C B then BC A. (f) For all sets A, B, if A Ç B then (AU B) – (An B) # 0.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 35E
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For each statement, Determine if it is True. If it is true then prove it. If it is False then disprove it or prove its negation. (a) For all n e Z²², if n is composite, then there exists an integer d such that dn and 1 < d< vd. (b) There exists a pair of integers x and y such that 8x + 14y = 1. (c) For all positive integers a, b, c if a|c and b|c then ab|c. (d) For all sets A, B,C, if AUC CBUC then AC B. (e) For all sets A, B, if A C B then BC A. (f) For all sets A, B, if A Ç B then (AU B) – (An B) + 0. 2.
Transcribed Image Text:For each statement, Determine if it is True. If it is true then prove it. If it is False then disprove it or prove its negation. (a) For all n e Z²², if n is composite, then there exists an integer d such that dn and 1 < d< vd. (b) There exists a pair of integers x and y such that 8x + 14y = 1. (c) For all positive integers a, b, c if a|c and b|c then ab|c. (d) For all sets A, B,C, if AUC CBUC then AC B. (e) For all sets A, B, if A C B then BC A. (f) For all sets A, B, if A Ç B then (AU B) – (An B) + 0. 2.
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