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Ex 1.4

Ex 1.4 ,1 (i)
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Chapter 1 Class 12 Relation and Functions

Serial order wise

Last updated at March 16, 2023 by Teachoo

Ex 1.4, 2 For each binary operation * defined below, determine whether * is commutative or associative. (iii) On Q, define a * b = ab/2 Check commutative * is commutative if a * b = b * a Since a * b = b * a β a, b β Q * is commutative a * b = ππ/2 b * a = ππ/2 = ππ/2 Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c = a * (b * c) β a, b, c β Q * is an associative binary operation (a * b)* c = (ππ/2) * c = (ππ/2 Γ π)/2 = πππ/4 a * (b * c) = a * (ππ/2) = (π Γ ππ/2)/2 = πππ/4