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Let * be a binary operation defined on Q. Find if the followin

Question

Let $$ be a binary operation defined on $Q$ . Find if the following binary operation is associative.
$a b = a - b + ab$ $\forall a, b \in Q$ .

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Emma Discussed

Let

*

be a binary operation defined on

Q

. Find if the following binary operation is associative.

a * b = a - b + ab

\forall a, b \in Q

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

For

*

to be associative

(a * b) * c = a * (b * c)

We have

L H S = (a * b) * c = (a - b + ab) * c = (a - b + ab) - c + (a - b + ab) c = a - b - c + ab + a c - b c + ab c

R H S = a * (b * c) = a * (b - c + b c) = a - (b - c + b c) + a (b - c + b c) = a - b + c - b c + ab - a c + ab c

Thus

L H S \neq = R H S

Hence

*

is not accociative.

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Question Text	Let $$ be a binary operation defined on $Q$ . Find if the following binary operation is associative. $a b = a - b + ab$ $\forall a, b \in Q$ .
Answer Type	Text solution:1
Upvotes	150