Sum

Examine whether the operation *defined on R by a * b = ab + 1 is (i) a binary or not. (ii) if a binary operation, is it associative or not?

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#### Solution

The given operation is a * b = ab + 1

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

Let a∈ R, b∈ R

then a*b∈ R

also ab +1 ∈ R

i.e. a *b ∈ R

so * on R satisfies the closure property

Now if this binary operation satisfies associative law then

(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

**∴ **(a * b) * c ≠ a * (b * c)

i.e., * operation does not follow associative law.

Concept: Concept of Binary Operations

Is there an error in this question or solution?

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