Q. 175.0( 1 Vote )

# Mark the tick against the correct answer in the following:Let a * b = a + ab for all a, b ∈ Q. Then,A. * is not a binary compositionB. * is not commutativeC. * is commutative but not associativeD. * is both commutative and associative

According to the question ,

Q = { a,b }

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

Formula

* is commutative if a * b = b * a

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

Check for commutative

Consider , a * b = a + ab

And , b * a = b + ba

Both equations will not always be true .

Therefore , * is not commutative ……. (1)

Check for associative

Consider , (a * b) * c = (a + ab) * c = a+ab + (a+ab)c=a+ab+ac+abc

And , a * (b * c) = a * (b+bc) = a+a(b+bc) = a+ab+abc

Both the equation are not the same and therefore will not always be true.

Therefore , * is not associative ……. (2)

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

Correct option will be (B)

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