Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
19. Evaluation of Proofs See the instructions for Exercise (19) on page 100 from Section 3.1. (a) Proposition. If m is an odd integer, then (m + 6) is an odd integer. Proof. For m + 6 to be an odd integer, there must exist an integer n such that m +6=2n + 1, By subtracting 6 from both sides of this equation, we obtain m = 2n – 6 † I = 2 (n=3) +1. By the closure properties of the integers, (n÷3) is an integer, and hence, the last equation implies that m is an odd integer. This proves that if m is an odd integer, then m + 6 is an oddinteger. (b) Proposition. For all integers m and n, if mn is an even integer, then m is even orn is even. Proof. For either m or n to be even, there exists an integer k such that m = 2k or n = 2k. So if we multiply m and n, the product will contain a factor of 2 and, hence, nn will be even.

19. Evaluation of Proofs See the instructions for Exercise (19) on page 100 from Section 3.1. (a) Proposition. If m is an odd integer, then (m + 6) is an odd integer. Proof. For m + 6 to be an odd integer, there must exist an integer n such that m +6=2n + 1, By subtracting 6 from both sides of this equation, we obtain m = 2n – 6 † I = 2 (n=3) +1. By the closure properties of the integers, (n÷3) is an integer, and hence, the last equation implies that m is an odd integer. This proves that if m is an odd integer, then m + 6 is an oddinteger. (b) Proposition. For all integers m and n, if mn is an even integer, then m is even orn is even. Proof. For either m or n to be even, there exists an integer k such that m = 2k or n = 2k. So if we multiply m and n, the product will contain a factor of 2 and, hence, nn will be 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 92E
See similar textbooks
icon
Related questions
Question
19 please
19. Evaluation of Proofs See the instructions for Exercise (19) on page 100 from Section 3.1. (a) Proposition. If m is an odd integer, then (m + 6) is an odd integer. Proof. For m + 6 to be an odd integer, there must exist an integer n such that m + 6 = 2n H 1, By subtracting 6 from both sides of this equation, we obtain m = 2n – 6 † I = 2 (n=3) +1. By the closure properties of the integers, (n+3) is an integer, and hence, the last equation implies that m is an odd integer. This proves that if m is an odd integer, then m + 6 is an odd integer. (b) Proposition. For all integers m and n, if mn is an even integer, then m 1s even or n is even. Proof. For either m or n to be even, there exists an integer k such that m = 2k or n = 2k. So if we multiply m and n, the product will contain a factor of 2 and, hence, nn will be even.
Transcribed Image Text:19. Evaluation of Proofs See the instructions for Exercise (19) on page 100 from Section 3.1. (a) Proposition. If m is an odd integer, then (m + 6) is an odd integer. Proof. For m + 6 to be an odd integer, there must exist an integer n such that m + 6 = 2n H 1, By subtracting 6 from both sides of this equation, we obtain m = 2n – 6 † I = 2 (n=3) +1. By the closure properties of the integers, (n+3) is an integer, and hence, the last equation implies that m is an odd integer. This proves that if m is an odd integer, then m + 6 is an odd integer. (b) Proposition. For all integers m and n, if mn is an even integer, then m 1s even or n is even. Proof. For either m or n to be even, there exists an integer k such that m = 2k or n = 2k. So if we multiply m and n, the product will contain a factor of 2 and, hence, nn will be even.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Basics of Inferential Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS