# Mark the tick against the correct answer in the following:Let Q+ be the set of all positive rationals. Then, the operation * on Q+ defined by for all a, b ∈ Q+ isA. commutative but not associativeB. associative but not commutativeC. neither commutative nor associativeD. both commutative and associative

According to the question ,

Q = { Positive rationals }

R = {(a, b) : a * b = ab/2 }

Formula

* is commutative if a * b = b * a

* is associative if (a * b) * c = a * (b * c)

Check for commutative

Consider , a * b = ab/2

And , b * a = ba/2

Both equations are the same and will always true .

Therefore , * is commutative ……. (1)

Check for associative

Consider , (a * b) * c = (ab/2) * c = = abc/4

And , a * (b * c) = a * (bc/2) = = abc/4

Both the equation are the same and therefore will always be true.

Therefore , * is associative ……. (2)

Now , according to the equations (1) , (2)

Correct option will be (D)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Functional Equations - JEE with ease48 mins
Drift velocity & its relation with currentFREE Class
Relation between electric field and potential34 mins
Relation between Electric field & Potential45 mins
Interactive Quiz on Drift velocity & its relation with current38 mins
Interactive quiz on Relation between electric field and potential43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses