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If a is any odd integer, then a + a is even. Use the properties of even and odd integers listed in Example 4.3.3 and repeated below to evaluate whether the statement is true or false. Indicate which properties you use to justify your reasoning. 1. The sum, product, and difference of any two even integers are even. 2. The sum and difference of any two odd integers are even. 3. The product of any two odd integers is odd. 4. The product of any even integer and any odd integer is even. 5. The sum of any odd integer and any even integer is odd. 6. The difference of any odd integer minus any even integer is odd. 7. The difference of any even integer minus any odd integer is odd. O The statement is true. a2 = a. a is a product of odd integers and thus is odd by property 3. Therefore, a? + a is a sum of odd integers and thus is even by property 2. O The statement is true. a² = a· a is a product of odd integers and thus is even by property 4. Therefore, a2 + a is a sum of an even and an odd integer and thus is even by property 2. O The statement is false, a? = a · a is a product of odd integers and thus is odd by property 3. Therefore, a2 + a is a sum of odd integers and thus is odd by property 4. O The statement is false, a² = a · a is a product of odd integers and thus is even by property 4. Therefore, a2 + a is a sum of an even and an odd integer and thus is odd by property 5.

If a is any odd integer, then a + a is even. Use the properties of even and odd integers listed in Example 4.3.3 and repeated below to evaluate whether the statement is true or false. Indicate which properties you use to justify your reasoning. 1. The sum, product, and difference of any two even integers are even. 2. The sum and difference of any two odd integers are even. 3. The product of any two odd integers is odd. 4. The product of any even integer and any odd integer is even. 5. The sum of any odd integer and any even integer is odd. 6. The difference of any odd integer minus any even integer is odd. 7. The difference of any even integer minus any odd integer is odd. O The statement is true. a2 = a. a is a product of odd integers and thus is odd by property 3. Therefore, a? + a is a sum of odd integers and thus is even by property 2. O The statement is true. a² = a· a is a product of odd integers and thus is even by property 4. Therefore, a2 + a is a sum of an even and an odd integer and thus is even by property 2. O The statement is false, a? = a · a is a product of odd integers and thus is odd by property 3. Therefore, a2 + a is a sum of odd integers and thus is odd by property 4. O The statement is false, a² = a · a is a product of odd integers and thus is even by property 4. Therefore, a2 + a is a sum of an even and an odd integer and thus is odd by property 5.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the following statement. If a is any odd integer, then a + a is even. Use the properties of even and odd integers listed in Example 4.3.3 and repeated below to evaluate whether the statement is true or false. Indicate which properties you use to justify your reasoning. 1. The sum, product, and difference of any two even integers are even. 2. The sum and difference of any two odd integers are even. 3. The product of any two odd integers is odd. 4. The product of any even integer and any odd integer is even. 5. The sum of any odd integer and any even integer is odd. 6. The difference of any odd integer minus any even integer is odd. 7. The difference of any even integer minus any odd integer is odd. O The statement is true. a2 = a· a is a product of odd integers and thus is odd by property 3. Therefore, a? + a is a sum of odd integers and thus is even by property 2. O The statement is true. a? = a · a is a product of odd integers and thus is even by property 4. Therefore, a2 + a is a sum of an even and an odd integer and thus is even by property 2. O The statement is false. a2 = a· a is a product of odd integers and thus is odd by property 3. Therefore, a2 + a is a sum of odd integers and thus is odd by property 4. O The statement is false. a2 = a · a is a product of odd integers and thus is even by property 4. Therefore, a2 + a is a sum of an even and an odd integer and thus is odd by property 5.
Transcribed Image Text:Consider the following statement. If a is any odd integer, then a + a is even. Use the properties of even and odd integers listed in Example 4.3.3 and repeated below to evaluate whether the statement is true or false. Indicate which properties you use to justify your reasoning. 1. The sum, product, and difference of any two even integers are even. 2. The sum and difference of any two odd integers are even. 3. The product of any two odd integers is odd. 4. The product of any even integer and any odd integer is even. 5. The sum of any odd integer and any even integer is odd. 6. The difference of any odd integer minus any even integer is odd. 7. The difference of any even integer minus any odd integer is odd. O The statement is true. a2 = a· a is a product of odd integers and thus is odd by property 3. Therefore, a? + a is a sum of odd integers and thus is even by property 2. O The statement is true. a? = a · a is a product of odd integers and thus is even by property 4. Therefore, a2 + a is a sum of an even and an odd integer and thus is even by property 2. O The statement is false. a2 = a· a is a product of odd integers and thus is odd by property 3. Therefore, a2 + a is a sum of odd integers and thus is odd by property 4. O The statement is false. a2 = a · a is a product of odd integers and thus is even by property 4. Therefore, a2 + a is a sum of an even and an odd integer and thus is odd by property 5.
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