Q. 125.0( 2 Votes )

Show that the rel

Answer :

To show an equivalence relation , We need to check for all Reflexivity, Symmetric and Transitivity


For Reflexivity:


Let aZ


Since, |a - a| = 0 is divisible by 4


Then (a, a)S


Therefore, S is reflexive


For Symmetric:


Let (a, b)S


Since, |a - b| is divisible by 4


And, |b - a| is also divisible by 4


So, (b, a)S


Hence, S is symmetric


For Transitivity:


Let (a, b)S and (b, c)S


Since, |a - b| and |b - c| are divisible by 4


And, |a - b| = 4p and |b - c| = 4q for some p, qZ


Then, |a - c| = |(a - b) + (b - c)| = 4(p + q)


|a - c| is divisible by 4


So, (a, c)S


As S is reflexive , symmetric and transitive its an equivalence relation.


Now,


Let (1, x) S , xA


x - 1 = 4p , for some pZ


z = 1 + 4p


if we put p = 1, 2 then


z = 5, 9


since, |1 - 0| is not divisible by 4, set of elements related to 1 is [5, 9]


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

State True Mathematics - Exemplar

State True Mathematics - Exemplar

State True Mathematics - Exemplar

Let A = {1, 2, 3}Mathematics - Exemplar

Show that the relMathematics - Board Papers

Let N denote the Mathematics - Board Papers