Question

Let * be any binary operation on the set R defined by a * b = a + b – ab, then the binary operation * is

• A. Associative
• B. Commutative and associative
• C. Commutative but not associative
• D. Commutative but not associative

Answer 1

The correct option is B

Commutative and associative

For commutativity:

a * b = a + b – ab and b * a = b + a – ba = a + b – ab

So, a * b = b * a. So, * is commutative.

For associativity:

a * (b * c) = a * (b + c – bc) = a + b + c – bc – ab – ac +abc, and

(a * b) * c = (a + b – ab) * c = a + b – ab + c – ac – bc + abc.

So, a * (b * c) = (a * b) * c.