Q. 185.0( 2 Votes )

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+ is

A. commutative but not associative

B. associative but not commutative

C. neither commutative nor associative

D. both commutative and associative

Answer :

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 easeFunctional Equations - JEE with easeFunctional Equations - JEE with ease48 mins
Drift velocity & its relation with currentDrift velocity & its relation with currentDrift velocity & its relation with currentFREE Class
Relation between electric field and potentialRelation between electric field and potentialRelation between electric field and potential34 mins
Relation between Electric field & PotentialRelation between Electric field & PotentialRelation between Electric field & Potential45 mins
Interactive Quiz on Drift velocity & its relation with currentInteractive Quiz on Drift velocity & its relation with currentInteractive Quiz on Drift velocity & its relation with current38 mins
Interactive quiz on Relation between electric field and potentialInteractive quiz on Relation between electric field and potentialInteractive 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
caricature
view all courses