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Whether binary commutative/associative or not
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Associative Binary Operations
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Whether binary commutative/associative or not
Last updated at May 29, 2023 by Teachoo
Question 19 Show that addition and multiplication are associative binary operation on R. But subtraction is not associative on R. Division is not associative on R∗. Addition * is associative if (a * b) * c = a * (b * c) Since (a * b) * c = a * (b * c) ∀ a, b, c ∈ R + is an associative binary operation Multiplication * is associative if (a * b) * c = a * (b * c) Since (a * b) * c = a * (b * c) ∀ a, b, c ∈ R × is an associative binary operation Subtraction * is associative if (a * b) * c = a * (b * c) Since (a * b) * c ≠ a * (b * c) ∀ a, b, c ∈ R – is not an associative binary operation Division * is associative if (a * b) * c = a * (b * c) Since (a * b) * c ≠ a * (b * c) ÷ is not an associative binary operation