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3. Prove that for any positive integer n, n is even if and only if 5n + 2 is even. Indicate which proof methods you used, as well as the assumptions (what you suppose) and the conclusions (what you need to show) of the proof.

3. Prove that for any positive integer n, n is even if and only if 5n + 2 is even. Indicate which proof methods you used, as well as the assumptions (what you suppose) and the conclusions (what you need to show) of the proof.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.6: The Binomial Theorem
Problem 54E
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Additional Topics: Proving biconditional statements To prove that a biconditional statement of the form p » q is true, you must prove that p → q and q - p are both true. For example, to prove that for any integer n, n is odd if and only if n? is odd, you must prove that (1) if n is odd, then n? is odd (see Example 2 in Lecture Slides 08), and (2) if n² is odd, then n is odd (see Exercise 10.2.1 in Lecture Slides 10). 3. Prove that for any positive integer n, n is even if and only if 5n + 2 is even. Indicate which proof methods you used, as well as the assumptions (what you suppose) and the conclusions (what you need to show) of the proof.
Transcribed Image Text:Additional Topics: Proving biconditional statements To prove that a biconditional statement of the form p » q is true, you must prove that p → q and q - p are both true. For example, to prove that for any integer n, n is odd if and only if n? is odd, you must prove that (1) if n is odd, then n? is odd (see Example 2 in Lecture Slides 08), and (2) if n² is odd, then n is odd (see Exercise 10.2.1 in Lecture Slides 10). 3. Prove that for any positive integer n, n is even if and only if 5n + 2 is even. Indicate which proof methods you used, as well as the assumptions (what you suppose) and the conclusions (what you need to show) of the proof.
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