The Total solution for NCERT class 6-12
Let┬аA┬аbe any set containing more than one element. Let тАШ*тАЩ be abinary operation on┬аA definedby┬аa┬а*┬аb┬а=┬аb┬аfor all┬аa,┬аb┬атИИ┬аA┬аIs тАШ*тАЩ commutative or associative on┬аA?
Let a, b тИИ A
Then, a * b = b
b * a = a
Therefore a * b тЙа b *a
Thus, * is notcommutative on A
Now we have to checkassociativity:
Let a, b, c тИИ A
a * (b * c) = a * c
= c
Therefore
a * (b * c) = (a * b)* c, тИА a, b, c тИИ A
Thus, * is associativeon A