Let Q+ be the set of all positive rational numbers.
(i) Show that the operation * on Q+ defined by is a binary operation.
(ii) Show that * is commutative.
(iii) Show that * is not associative.
(i) * is an operation as where a, b ∈ Q+. Let and b = 2 two integers.
So, * is a binary operation from .
(ii) For commutative binary operation, a*b = b*a.
Since a*b = b*a, hence * is a commutative binary operation.
(iii) For associative binary operation, a*(b*c) = (a*b) *c.
As a*(b*c) ≠(a*b) *c, hence * is not associative binary operation.
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