Let ∗ be a binary operation on the set Q of rational numbers as follows:(i) a ∗ b = a – b. (ii) a ∗ b = a2 + b2(iii) a ∗ b = a + ab. (iv) a ∗ b = (a – b)2(v) a ∗ b = ab/4(vi) a ∗ b = ab2Find which of the binary operations are commutative and which are associative.
Let ∗ be a binary operation on the set Q of rational numbers as follows:(i) a ∗ b = a – b. (ii) a ∗ b = a2 + b2(iii) a ∗ b = a + ab. (iv) a ∗ b = (a – b)2(v) a ∗ b = ab/4(vi) a ∗ b = ab2Find which of the binary operations are commutative and which are associative.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 12E
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Let ∗ be a binary operation on the set Q of rational numbers as follows:
(i) a ∗ b = a – b. (ii) a ∗ b = a2 + b2
(iii) a ∗ b = a + ab. (iv) a ∗ b = (a – b)2
(v) a ∗ b = ab/4
(vi) a ∗ b = ab2
Find which of the binary operations are commutative and which are associative.
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