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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