Question

Determine whether each of the following relations are reflexive, symmetric and
transitive:

(ii) Relation R in the set N of natural numbers defined as
R = {(x, y): y = x + 5 and x <4}​

Answer 1

Answer:

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) Relative R in the set N of natural numbers defined as

R={(x,y):y=x+5 andx<4}

(iii) Relation R in the set A={1,2,3,4,5,6} as

R={(x,y):yis divisible byx}

(iv) Relative 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):xandywork at the same place }

(b)R={(x,y):xandylive in the same locality}

(c)R={(x,y):xis exactly7cm taller thany}

(d)R={(x,y):xis wife ofy}

(e)R={(x,y):x is father ofy}