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Question

On the set Qof all rational numbers the operation * which is both associative and commutative is given by a*b, is


A

a+b+ab

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B

a2+b2

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C

ab+1

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D

2a+3b

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Solution

The correct option is A

a+b+ab


Explanation for the correct option:

Checking the associative and commutative properties for the expression:

Let us assume, from the first option

a*b=a+b+ab

Now, from the above expression

a*b*c=a*b+c+bc=a+b+c+ab+ac+abc=a+b+ab+c+ac+abc=a*b*c

So, it is associative,

And now,

a*b=a+b+ab=b+a+ba=b*a

Also, it is commutative.

Therefore, the correct answer is option (A).


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