Answer :

It is given that On Z+, define a b = ab

abϵ Z+, so operation * is binary


We know that ab = ba for a, b ϵ Z+


1 * 2 =12 and 2 * 1 = 21 =2


1 * 2 ≠ 2 *1, where 1,2 ϵ Z+


The operation * is not commutative.


Also, we get,


(1 * 2) * 3 = 23 *3 = 8 * 3 = 24


1 * (2 * 3) = 1 * 32 = 1 * 9 = 9


(1 * 2) * 3 ≠ 1 * (2 * 3), where 1,2,3 ϵ Z+


The operation * 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
caricature
view all courses
RELATED QUESTIONS :

Fill in theMathematics - Exemplar

Let f : [2, ∞) <sMathematics - Exemplar

Let f : N Mathematics - Exemplar

Fill in theMathematics - Exemplar

Let f :R →<Mathematics - Exemplar

Let f : [0, 1] <sMathematics - Exemplar

Which of the follMathematics - Exemplar