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Definition: For integers a and b, we say that a divides b (written as a|b) if there exists an integer q such that b = aq. Prove that the following statements are false: (a) 541 (b) Vn N, 8|n if and only if 4|n2 (c) If x > 0, y > 0, then (x+5)2 + (y +12)² < 132 Write the negation for question 1c). Let n Z. Prove that n² is even if and only if n is even.

Definition: For integers a and b, we say that a divides b (written as a|b) if there exists an integer q such that b = aq. Prove that the following statements are false: (a) 541 (b) Vn N, 8|n if and only if 4|n2 (c) If x > 0, y > 0, then (x+5)2 + (y +12)² < 132 Write the negation for question 1c). Let n Z. Prove that n² is even if and only if n is even.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 90E
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Definition: For integers a and b, we say that a divides b (written as a|b) if there exists an integer q such that b = aq. Prove that the following statements are false: (a) 541 (b) Vn N, 8|n if and only if 4|n2 (c) If x > 0, y > 0, then (x+5)2 + (y +12)² < 132 Write the negation for question 1c). Let n Z. Prove that n² is even if and only if n is even.
Transcribed Image Text:Definition: For integers a and b, we say that a divides b (written as a|b) if there exists an integer q such that b = aq. Prove that the following statements are false: (a) 541 (b) Vn N, 8|n if and only if 4|n2 (c) If x > 0, y > 0, then (x+5)2 + (y +12)² < 132 Write the negation for question 1c). Let n Z. Prove that n² is even if and only if n is even.
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