Q. 2 A4.3( 21 Votes )

# For each operatio

Answer :

It is given that On Z, define a b = a – b

a –b ϵ Z. so the operation * is binary.

We can see that 1 * 2 = 1-2 = -1 and 2 * 1 = 2-1 = 1.

1 *2 ≠ 2 * 1, where 1,2 ϵ Z.

the operation * is not commutative.

Also, we get,

(1 * 2) * 3 = (1 – 2) * 3 = -1 * 3 = -1 -3 = -4

1 * (2 * 3) = 1 * (2 – 3) = 1 * -1 = 1 – (-1) = 2

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 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