[(iv)" Relation "R" in the set "Z" of all integers defined as "],[qquad R={(x,y):x-y" is an integer "}]

Determine whether each of the following relations is reflexive, symmetric and transitive. Relation R in the set Z of all integers defined as R = {(x,y) :x-y is an integer}

Determine whether each of the following relations are reflexive , symmetric and transitive : Relation R in the set Z of all integers defined as ={ (x,y) : x - y is an integers }

Determine whether each of the following relations are reflexive, symetric and transitive Relation R in the set Z of all integers defined as R = (x,y) : x-y is an integer.

Determine whether each of the following relations are reflexive, symmetric and transitive : (i) Relation R in the set A = {1, 2, 3,......, 13, 14} defined as R={(x,y): 3x-y=0} (ii) Relation R in the set N of natural numbers defined as R={(x,y): y=x+5 " and " x lt 4} (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} defined as R = {(x, y): y is divisible by x}. iv) Relation R in the set Z, of all integers defined as R = {(x, y) : x -y is an integer}.

Determine whether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A = {1, 2, 3, ..., 13, 14} defined as R = {(x, y) : 3x – y = 0} (ii) Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x lt 4} (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x } (iv) Relation R in the set Z of all integers defined as R = {(x, y) : x – y is an integer} (v) Relation R in the set A of human beings in a town at a particular time given by (a) R = {(x, y) : x and y work at the same place} (b) R = {(x, y) : x and y live in the same locality} (c) R = {(x, y) : x is exactly 7 cm taller than y } (d) R = {(x, y) : x is wife of y } (e) R = {(x, y) : x is father of y }

Show that the relation R defined on the set Z of all integers defined as R={(x,y):x-y is an integer} is reflexive, symmertric and transtive.

Let R be the relation in the set Z of all integers defined by R= {(x,y):x-y is an integer}. Then R is

Determine whether Relation R on the set Z of all integer defined as R={(x ,\ y): (x-y) =i n t e g e r} is reflexive, symmetric or transitive.

Prove that the relation R in the set of integers z defined by R = { ( x , y) : x-y is an integer } is an equivalence relation.