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.
(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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