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Prove each of the following statements c) Prove that if a is an integer, then a² + a is even. [Hint: Use proof by cases.] d) Prove that a + b is even if and only if a and b are both even or both odd.

Prove each of the following statements c) Prove that if a is an integer, then a² + a is even. [Hint: Use proof by cases.] d) Prove that a + b is even if and only if a and b are both even or both odd.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 2TFE: Label each of the following statement as either true or false. 2. Let b be any integer. Then 0b.
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Prove each of the following statements c) Prove that if a is an integer, then a² + a is even. [Hint: Use proof by cases.] d) Prove that a + b is even if and only if a and b are both even or both odd.
Transcribed Image Text:Prove each of the following statements c) Prove that if a is an integer, then a² + a is even. [Hint: Use proof by cases.] d) Prove that a + b is even if and only if a and b are both even or both odd.
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