Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(a) Let * be defined on Z by a * b = 2ab. Determine whether the binary operator defined is commutative and/or associative. (b) On Z, define * by a * b = a – b. Determine whether the definition of * does give a binary operation on a set. In the event that * is not a binary operation, write down the condition which was violated. (c) Prove that if * is an associative and commutative binary operation on a set S, then (a * b) * (c * d) [(d * c) * a] * b for all a, b, c,d e S.

(a) Let * be defined on Z by a * b = 2ab. Determine whether the binary operator defined is commutative and/or associative. (b) On Z, define * by a * b = a – b. Determine whether the definition of * does give a binary operation on a set. In the event that * is not a binary operation, write down the condition which was violated. (c) Prove that if * is an associative and commutative binary operation on a set S, then (a * b) * (c * d) [(d * c) * a] * b for all a, b, c,d e S.

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
100%
(a) Let * be defined on Z by a * b = 2ab, Determine whether the binary operator defined is commutative and/or associative. %3D (b) On Z, define by a * b = a- b. Determine whether the definition of * does give a binary operation on a set. In the event that * is not a binary operation, write down the condition which was violated. (c) Prove that if * is an associative and commutative binary operation on a set S, then (a * b) * (c * d) = [(d* c) * a] * b for all a, b, c,d e S.
Transcribed Image Text:(a) Let * be defined on Z by a * b = 2ab, Determine whether the binary operator defined is commutative and/or associative. %3D (b) On Z, define by a * b = a- b. Determine whether the definition of * does give a binary operation on a set. In the event that * is not a binary operation, write down the condition which was violated. (c) Prove that if * is an associative and commutative binary operation on a set S, then (a * b) * (c * d) = [(d* c) * a] * b for all a, b, c,d e S.
Expert Solution
steps

Step by step

Solved in 4 steps with 4 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