Theorem: "n and m are even numbers = n × m is an even number." Proof: Any even number a can be presented in the form a = 2k, where k is some integer number, therefore, let us write n and m in the form = 2k1, m = 2k2, where k1, k2 are integers. The product is m x n = (2kj) × (2k2) = 2 × (2k,k2). Since k1, k2 are integer numbers, the twi the product of them will also be some integer number k3 = 2k,k2. Thus, m x n = 2k3, where k3 is an integer, therefore the product of the integers n and m is even.
Theorem: "n and m are even numbers = n × m is an even number." Proof: Any even number a can be presented in the form a = 2k, where k is some integer number, therefore, let us write n and m in the form = 2k1, m = 2k2, where k1, k2 are integers. The product is m x n = (2kj) × (2k2) = 2 × (2k,k2). Since k1, k2 are integer numbers, the twi the product of them will also be some integer number k3 = 2k,k2. Thus, m x n = 2k3, where k3 is an integer, therefore the product of the integers n and m is even.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
provide solution/explanation
Transcribed Image Text:Theorem: "n and m are even numbers =nxm is an even number."
Proof:
Any even number a can be presented in the form a = 2k, where k is some integer number, therefore, let us write n and m in the form n
= 2k1, m = 2k2, where k1, k2 are integers. The product is m x n = (2kj) × (2k2) = 2 × (2k,k2). Since k1, k2 are integer numbers, the twice
the product of them will also be some integer number k3 = 2kkɔ. Thus, m x n = 2k3, where k3 is an integer, therefore the product of
the integers n and m is even.
The reasoning used here is
O equivalence proof
O backward reasoning
O reductio ad absurdum.
O forward reasoning
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
