Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let c, d be integers. Prove the following statement by contrapositive: If c – 6d is ODD, then c is ODD.

Let c, d be integers. Prove the following statement by contrapositive: If c – 6d is ODD, then c is ODD.

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

q1

Let c, d be integers. Prove the following statement by contrapositive: If c – 6d is ODD, then c is ODD. |
Transcribed Image Text:Let c, d be integers. Prove the following statement by contrapositive: If c – 6d is ODD, then c is ODD. |
Expert Solution
Step 1

Given c, d be integers.

We have to prove that the statement, "if c2-6d is odd then c is odd" by contrapositive.

Let c is not odd that is c is even

Then c can be written as c=2m, where m is integer.

Now,

c2-6d=2m2-6d=4m2-6d=22m2-3d

Since, 2m2-3d is an integer

Then 22m2-3d is an even integer.

Hence, c2-6d is even integer.

Which is a contradiction because given c2-6d is odd.

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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