(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
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(bc+1) + 1
Since (a*b) *c≠ a*(b*c), therefore * is not associative.
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