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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.

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