Equivalence relation

Question

Q)Which of the following is not an equivalence relation on a set of all real numbers?

A) R1 = { (a,b) / a-b is a integer }

B) R2 = { (a,b) / a-b is divisible by 5 }

C) R3 = { (a,b) / a-b  is  an odd number }

D) R4 = { (a,b) / a-b is an even number }

Comments

i mean properties must be applicable to all elements in R₁

so it is always better to find elements which does not satisfy properties

---

If any pair belongs to the relation then I check all of the three conditions.

i.e. (1,1.5) =>    1 - 1.5 = - 0.5

     (2,3.6) =>    2 - 3.6 = -1.4 does not belong to the relation, so these pairs I not checked the condition.

please correct me if I'm wrong

---

Lakshman Patel RJIT yes obviously check the properties for the pairs which are in the relation

Answer 1

option C 

Reflexive and transative property is fail here.

example

for reflexive: (1,1) . it become 0 which is not an odd .

for transative: (5,2) is odd

                         (2,1)is odd

                  but (5,1) is not an odd .

Comments

Good abhishekmehta4u

Answer 2

before checking if relation R1 is equivalence or not, First create R1, as the condition says a-b is an integer so (1,0.5) is not an integer so it will not be in R1 at all
sample R1 would be
R1={---(-1,-1),(-1,0),------(1,1),(2,2),(3,3),(4,4),(5,5),(1,5),-------}
so now we have R1, check for reflexive,symmetric,transitive