Q. 45.0( 1 Vote )

Determine whether

Answer :

For the binary operation * on set N to be associative the following equation should hold true


x*(y*z) = (x*y) *z for all x, y, z N


let us first find x*(y*z)


As a*b = 2ab


x*(y*z) = x*(2yz)



Now let us find (x*y) *z


(x*y) *z = (2xy) *z



Comparing (i) and (ii) we have x*(y*z) ≠ (x*y) *z


Hence the binary operation * on set N is not associative


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