Ex 1.4, 2 (v) - Chapter 1 Class 12 Relation and Functions

Last updated at April 16, 2024 by Teachoo

Ex 1.4, 2 - Chapter 1 Class 12 Relation and Functions - Part 9

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Transcript

Ex 1.4, 2 For each binary operation * defined below, determine whether * is commutative or associative. (v) On Z+, define a * b = 𝑎^𝑏 Check commutative * is commutative if a * b = b * a Since a * b ≠ b * a * is not commutative a * b = 𝑎^𝑏 b * a = 𝑏^𝑎 Check associative * is associative if (a * b) * c = a * (b * c) Example Let a = 2, b = 3, c = 4 (a * b)* c = (𝑎^𝑏) * c = (𝑎^𝑏 )^𝑐 a * (b * c) = a * (2^𝑏𝑐) = 2^(𝑎2^𝑏𝑐 ) (a * b)* c = (2 * 3) * 4 = (2^3) * 4 = 8 * 4 = 8^4 a * (b * c) = 2 * (3 * 4) = 2 * (3^4) = 2 * 81 = 2^81 Since (a * b) * c ≠ a * (b * c) * is not an associative binary operation

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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