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Verify whether the operation * defined on Q by a*b = ab/2 is associative or not. |
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Answer» * is defined on Q by a*b = ab/2 for associative we have to prove that a* (b* c) = (a* b)* c ∴ a*(b*c) = a * ab/2 b*c = bc/2 = abc/4 ……….. (1) (a*b)*c = ab/2 *c = abc/4 ……….. (2) ∴ from (1) and (2) ∴ * is Associative ∴ * Satisfies the associative property. |
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