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8. Which of the following best characterizes the statements, where P and Q are statements A) If m is an even integer and n is an odd integer, then m + n is an odd integer B) If m is an even integer and n is an odd integer, then m x n is an even integer a. Only A is true b. Only B is true c. Both A and B are true d. Both A and B are false

8. Which of the following best characterizes the statements, where P and Q are statements A) If m is an even integer and n is an odd integer, then m + n is an odd integer B) If m is an even integer and n is an odd integer, then m x n is an even integer a. Only A is true b. Only B is true c. Both A and B are true d. Both A and B are false

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Question 8: Logical Reasoning with Integer Properties** **Which of the following best characterizes the statements, where P and Q are statements:** A) If \( m \) is an even integer and \( n \) is an odd integer, then \( m + n \) is an odd integer B) If \( m \) is an even integer and \( n \) is an odd integer, then \( m \times n \) is an even integer a. Only A is true b. Only B is true c. Both A and B are true d. Both A and B are false --- **Explanation:** - Statement A examines the sum of an even integer and an odd integer. - If \( m \) is an even integer (e.g., 2, 4, 6) and \( n \) is an odd integer (e.g., 1, 3, 5), then their sum (\( m + n \)) will always be an odd integer. Therefore, statement A is true. - Statement B examines the product of an even integer and an odd integer. - If \( m \) is an even integer and \( n \) is an odd integer, then their product (\( m \times n \)) will always be an even integer. This is due to the nature of multiplication where multiplying by even number always results in an even product. Therefore, statement B is true. Since both statements A and B are true, the correct choice is: **c. Both A and B are true**
Transcribed Image Text:**Question 8: Logical Reasoning with Integer Properties** **Which of the following best characterizes the statements, where P and Q are statements:** A) If \( m \) is an even integer and \( n \) is an odd integer, then \( m + n \) is an odd integer B) If \( m \) is an even integer and \( n \) is an odd integer, then \( m \times n \) is an even integer a. Only A is true b. Only B is true c. Both A and B are true d. Both A and B are false --- **Explanation:** - Statement A examines the sum of an even integer and an odd integer. - If \( m \) is an even integer (e.g., 2, 4, 6) and \( n \) is an odd integer (e.g., 1, 3, 5), then their sum (\( m + n \)) will always be an odd integer. Therefore, statement A is true. - Statement B examines the product of an even integer and an odd integer. - If \( m \) is an even integer and \( n \) is an odd integer, then their product (\( m \times n \)) will always be an even integer. This is due to the nature of multiplication where multiplying by even number always results in an even product. Therefore, statement B is true. Since both statements A and B are true, the correct choice is: **c. Both A and B are true**
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