Determine whether each of the following relations are reflexive, symmetric and transitive:
Channel: Doubtnut
Date: 2020-07-05

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 â€“ 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 â€“ 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}