Q. 115.0( 2 Votes )

# 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.

Answer :

(i)Let a = 1, b = 2Q ^{+}

a*b = = 1.5Q ^{+}

* is closed and is thus a binary operation on Q ^{+}

(ii) a*b = = 1.5

And b*a = = 1.5

Hence * is commutative.

(iii)let c = 3.

(a*b)*c = 1.5*c =

a*(b*c) = a* = 1*2.5 = = 1.75

hence * is not associative.

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