Determine whether the given definition of ∗ give a binary operation on the given set. If so, check whether ∗ is i) commutative ii) associative? Also, examine ∗ for identity element? a. On Z + , a ∗ b = 2^ab b. On Q, a ∗ b = ?b/2 c. On Z + , a ∗ b =a^b

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 13E: Assume that is an associative binary operation on the non empty set A. Prove that a[ b(cd) ]=[...
icon
Related questions
Question
Determine whether the given definition of ∗ give a binary operation on the given set. If so, check whether ∗ is i) commutative ii) associative? Also, examine ∗ for identity element? a. On Z + , a ∗ b = 2^ab b. On Q, a ∗ b = ?b/2 c. On Z + , a ∗ b =a^b
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 7 steps

Blurred answer
Knowledge Booster
Complexity
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax