The document defines a relation R on real numbers where x is related to y if x-y is an integer. It then proves R is an equivalence relation by showing it is reflexive, symmetric, and transitive: it is reflexive because subtracting a number from itself is 0, an integer; it is symmetric because subtracting y from x gives the negation of x-y, also an integer; and it is transitive because the difference of the sums of subtracting integers must also be an integer.

1. For all x,y epsilon R define a relation R to be Prove R is on equivalence Relation?
Solution
reflexive: a-a =0 which is in integers symmetric: a-b is integer then b-a= the
negation of that integer which is also an integer transitive: a-b is integer and b-c is integer a-b+b-
c=a-c must be an integer