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For Each Binary Operation * Defined Below, Determine Whether * is Commutative Or Associative. - CBSE (Commerce) Class 12 - Mathematics

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Question

For each binary operation * defined below, determine whether * is commutative or associative.

On − {−1}, define `a*b = a/(b+1)`

Solution

On R, * − {−1} is defined by `a * b = a/(b + 1)`

It can be observed that `1*2 = 1/(2+1) = 1/3` and 

`2 * 1  = 2/(1 + 1) = 2/2 = 1`

∴1 * 2 ≠ 2 * 1 ; where 1, 2 ∈ − {−1}

Therefore, the operation * is not commutative.

It can also be observed that:

`(1 * 2) * 3 = 1/3 * 3 = (1/3)/(3+1) = 1/12`

`1 * ( 2 * 3) = 1 * 2/(3+1) =  1 * 2/4 = 1 * 1/2 = 1/(1/2 +   1) = 1/(3/2) = 2/3`

∴ (1 * 2) * 3 ≠ 1 * (2 * 3) ; where 1, 2, 3 ∈ − {−1}

Therefore, the operation * is not associative.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 1: Relations and Functions
Q: 2.6 | Page no. 24
Solution For Each Binary Operation * Defined Below, Determine Whether * is Commutative Or Associative. Concept: Concept of Binary Operations.
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