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 = 2
Q +
a*b = 
= 1.5
Q +
* 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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