Q. 95.0( 1 Vote )

Let * be a binary

To prove: * is neither commutative nor associative

Let us assume that * is commutative

ab = ba for all a,b N

This is valid only for a = b

For example take a = 1, b = 2

12 = 1 and 21 = 2

So * is not commutative

Let us assume that * is associative

(ab)c for all a,b,c N

for all a,b,c N

This is valid in the following cases:

(i) a = 1

(ii) b = 0

(iii) bc = bc

For example, let a = 2,b = 1,c = 3

abc = 2(1 × 3) = 23 = 8

= 2

So * is not associative

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
RELATED QUESTIONS :

| Let * be a binaMathematics - Board Papers

Find the idMathematics - Board Papers

Let f : A Mathematics - Exemplar

Show that the binMathematics - Board Papers

Determine whetherRD Sharma - Volume 1

Fill in theMathematics - Exemplar