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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 11E
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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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