The Total solution for NCERT class 6-12
Let A be any set containing more than one element. Let ‘*’ be abinary operation on A definedby a * b = b for all a, b ∈ A Is ‘*’ commutative or associative on A?
Let a, b ∈ A
Then, a * b = b
b * a = a
Therefore a * b ≠ b *a
Thus, * is notcommutative on A
Now we have to checkassociativity:
Let a, b, c ∈ A
a * (b * c) = a * c
= c
Therefore
a * (b * c) = (a * b)* c, ∀ a, b, c ∈ A
Thus, * is associativeon A