# Q. 9 Let ∗ be a binary operation on the set Q of rational numbers as follows:(vi) Find which of the binary operations are commutative and which are associative.

On the set Q ,the operation * is defines as   .It is observed that:

For

for

Hence, the * operation is not  commutative.

It can be observed that

for all

The operation * is  not associative.

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