Let A be any set containing more than one element. Let ‘*’ be a

1.	Let A be any set containing more than one element. Let ‘’ be a binary operation on A defined by a b = b for all a, b ∈ A Is ‘*’ commutative or associative on A?
Answer» Let a, b ∈ A Then, a * b = b b * a = a So, a * b ≠ b * a Thus, * is not commutative on A Let us check associativity: Let a, b, c ∈ A a * (b * c) = a * c = c So a * (b * c) = (a * b) * c, ∀ a, b, c ∈ A Hence, * is associative on A

Let A be any set containing more than one element. Let ‘’ be a binary operation on A defined by a b = b for all a, b ∈ A Is ‘*’ commutative or associative on A?

Answer»

Let a, b ∈ A

Then, a * b = b

b * a = a

So, a * b ≠ b * a

Thus, * is not commutative on A

Let us check associativity:

Let a, b, c ∈ A

a * (b * c) = a * c

= c

a * (b * c) = (a * b) * c, ∀ a, b, c ∈ A

Hence, * is associative on A