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Question

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


A

Associative

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B

Commutative and associative

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C

Commutative but not associative

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D

Commutative but not associative

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Solution

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.


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