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Prove that the product of two odd integers is odd

Mathematics: A Discrete Introduction | 3rd Edition | ISBN: 9780840049421 | Authors: Edward A. Scheinerman ISBN: 9780840049421 447

Solution for problem 5.6 Chapter 5

Mathematics: A Discrete Introduction | 3rd Edition

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Mathematics: A Discrete Introduction | 3rd Edition | ISBN: 9780840049421 | Authors: Edward A. Scheinerman

Mathematics: A Discrete Introduction | 3rd Edition

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Problem 5.6

Prove that the product of two odd integers is odd.

Step-by-Step Solution:
Step 1 of 3

1.5 Exponents and Radicals Math 1315-003 Shelley Hamilton Division with Exponents:  5^7/5^4 = 5^7-4 = 5^3  (-8) ^10/ (-8) ^5 = (-8) ^10-5 = (-8) ^5  (3c) ^9/(3c) ^3 = (3c) ^9-3 = (3c) ^6  (7*19) ^3 = (7*19) (7*19) (7*19) = 7*7*7*19*19*19 = 7^3 * 19^3 When dividing exponents, you just subtract the exponents as you can see in the examples above. Product to a power:  (ab)^n = a^n * b^n  Ex. (5y) ^3 = 5^3 y^3 = 125y^3  (c^2 d^3) ^4 = (c^2) ^4 (d^3) ^4  (x/2) ^6 = x^6/2^6 = x^6/64  (a^4/b^3) ^3 = a^12/b^9  When multiplying when there is an exponent in and one outside of the (). You multiply them together. Also, that exponent outside of the parenthesis, you distribute it in with the coefficient. Or every variable in the parentheses. Quotient to a Power:  (a/b) ^n = a^n/b^n  Same here you distribute the exponent outside of the parentheses into each variable. Negative Exponent:  a^-n = 1/a^n  3^-2 = 1/3^2 = 1/9  5^-4 = 1/5^4 = 1/625  X^-1 = 1/x^1 = 1/x  -4^-2 = -1/4^2 = 1/16  When dealing with negative exponents, to make the exponent positive you simply just put a one over it and it will make the exponents positive as you can see in the examples above. Inversion Property:  (a/b) ^-n = (b/a) ^n  Ex. (5/8) ^-1 = 8/5  (1/2) ^-5 = (2/1) ^5 = 2^5/1^5 = 32/1  (2/5) ^-3 = (5/2) ^3 = 5^3/2^3 = 125/8  (3/x) ^-5 = (x/3) ^5 = x^5/3^5 = x^5/243  When dealing with inverse properties. You simply just change the proble

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Chapter 5, Problem 5.6 is Solved
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Textbook: Mathematics: A Discrete Introduction
Edition: 3
Author: Edward A. Scheinerman
ISBN: 9780840049421

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Prove that the product of two odd integers is odd