If relation R defined on set A is an equivalence relation, then R is

In order that a relation R defined on a non-empty set A is an equivalence relation, it is sufficient, if R

Prove that on the set of integers. Z, the relation R defined as aRb hArr a = +-b is an equivalence relation .

Prove that the following relation R in Z of integers is an equivalence relation : R = [ (x, y) : x - y is an integer}

Prove that the following relation R in Z of integers is an equivalence relation : R = [ (x, y) : 2x - 2y is an integer}

Prove that the following relation R in Z of integers is an equivalence relation : R = [ (x, y) : 3x- 3y is an integer}

Prove that the following relation R in Z of integers is an equivalence relation R = {(x, y): x-y is an integer}

Statement-1: The relation R on the set N xx N defined by (a, b) R (c, d) iff a+d = b+c for all a, b, c, d in N is an equivalence relation. Statement-2: The intersection of two equivalence relations on a set A is an equivalence relation.

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; S={(m/n , p/q)"m , n , p and q are integers such that n ,q"!="0 and q m = p n"} . Then (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation

Consider the set A=(a,b,c). Give an example of a relation R on A which is an equivalent relation.