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?

Commutativity: Let a, b . Then, a ^* b=b b ^* a=a Therefore, a ^* b ^* a Thus, * is not commutative on A. Associativity: Let a, b, c . Then, a ^* (b ^* c)=a ^* c =c (a ^* b) ^* c=b ^* c =c Therefore,a ^* (b ^* c)=(a ^* b) ^* c, a, b, c Thus, * is associative on A.

Let A be any set containing more than one element. Let '*' be a b…

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