Answer :

*: a*b=ab+1


(i) Given operation is a*b=ab+1

If any operation is a binary operation, it must follow closure property.

Let a∈R and b∈R

Then ab∈R

Also ab+1 ∈R

So, a*b ∈R

So * satisfies the closure property.

Since * is defined for all a, b
R, therefore * is a binary operation.


(ii) For * to be associative, (a*b) *c=a*(b*c)

(a*b) *c=(ab+1) *c

= (ab +1)c + 1

=abc+c + 1

a*(b*c) =a*(bc+1)

= a(bc+1) + 1

=abc+a+1

Since (a*b) *c≠ a*(b*c), therefore * is not associative.

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