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Question 4

Last updated at Dec. 21, 2017 by

Determine whether the binary operation * on the set N of natural numbers defined by a*b = 2 ab is associative or not.

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Question 4 Determine whether the binary operation * on the set N of natural numbers defined by a*b = 2ab is associative or not. * 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^(𝑎 ×(2^𝑏𝑐)) Note: You can take an example as well Find (1 * 2) * 3 & 1 * (2 * 3), and prove them not equal

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