Let R be the relation in the set Z of al...

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

reflexive

symmetric

transitive

an equivalence relation

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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 }

Determine whether Relation R on the set Z of all integer defined as R={(x,y):y is divisible by x}

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Let R be a relation on the set of integers given by aRb hArr a2^(k).b for some integer k. Then,R is

Let n be a positive integer.Prove that the relation R on the set Z of all integers numbers defined by (x,y)in R hArr x-y is divisible by n, is an equivalence relation on Z .

Let R be a relation defined on the set Z of all integers and xRy when x+2y is divisible by 3.then

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R relation on the set Z of integers and it is given by (x,y)in R hArr|x-y|<=1 then ,R is

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