Answer of this question

Let x ∊ Z
(x-x)=0, which is an integer.
⇒(x,x) ∊ R
∴R is reflexive.

Let x,y ∊ Z
Let (x,y) ∊ R
⇒(x-y) is an integer
⇒-(-x y) i.e. (y-x) is also an integer
⇒(y,x) ∊ R
∴R is symmetric

Let x,y,z ∊ Z
Let (x,y),(y,z) ∊ R
⇒(x-y) and (y-z) is an integer
⇒(x-y y-z) i.e (x-z) is also an integer
⇒(x,z) ∊ R
∴R is transitive

Hence, R is an equevalence relation.

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Written on March 21, 2017, 10:26 p.m.