Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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
See similar textbooks
icon
Related questions
Question
**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**
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS