Question 1. 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 as 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}