Question 1, Exercise 1.1, Class 12 mathematics

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 < 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}