Ex 1.4, 2 For each binary operation * defined below, determine whether * is commutative or associative. (iv) On Z+, define a * b = 2^𝑎𝑏 Check commutative * is commutative if a * b = b * a Since a * b = b * a ∀ a, b, c ∈ Z+ * is commutative a * b = 2^𝑎𝑏 b * a = 2^𝑏𝑎 = 2^𝑎𝑏 Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c ≠ a * (b * c) * is not an associative binary operation (a * b)* c = (2^𝑎𝑏) * c = 2^(2^𝑎𝑏 𝑐) a * (b * c) = a * (2^𝑏𝑐) = 2^(𝑎2^𝑏𝑐 )

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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