Determine whether each of the following relations are reflexive

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

1. Determine whether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set

\mathrm{A}=\{1,2,3, \ldots, 13,14\}

defined as

\mathrm{R}=\{(x, y): 3 x-y=0\}

(ii) Relation R in the set

\mathbf{N}

of natural numbers defined as

\mathrm{R}=\{(x, y): y=x+5 \text { and } x<4\}

(iii) Relation R in the set

\mathrm{A}=\{1,2,3,4,5,6\}

\mathrm{R}=\{(x, y): y \text { is divisible by } x\}

(iv) Relation R in the set

\mathbf{Z}

of all integers defined as

\mathrm{R}=\{(x, y): x-y \text { is an integer }\}

(1) (i) Relation R in the set

\mathrm{A}=\{1,2,3, \ldots, 13,14\}

defined as

\mathrm{R}=\{(x, y): 3 x-y=0\}

(2) (ii) Relation R in the set

\mathbf{N}

of natural numbers defined as

\mathrm{R}=\{(x, y): y=x+5 \text { and } x<4\}

(3) (iii) Relation R in the set

\mathrm{A}=\{1,2,3,4,5,6\}

\mathrm{R}=\{(x, y): y \text { is divisible by } x\}

(4) (iv) Relation R in the set

\mathbf{Z}

of all integers defined as

\mathrm{R}=\{(x, y): x-y \text { is an integer }\}

(5) (v)(a) Relation R in the set A of human beings in a town at a particular time given by

\mathrm{R}=\{(x, y): x

and

y

work at the same place \} (6) (v)(b) Relation R in the set A of human beings in a town at a particular time given by

\mathrm{R}=\{(x, y): x

and

y

live in the same locality \} (7) (v)(c) Relation R in the set A of human beings in a town at a particular time given by

\mathrm{R}=\{(x, y): x

is exactly 7 cm taller than

y\}

(8) (v)(d) Relation R in the set A of human beings in a town at a particular time given by

\mathrm{R}=\{(x, y): x

is wife of

y\}

(9) (v)(e) Relation R in the set A of human beings in a town at a particular time given by

\mathrm{R}=\{(x, y): x

is father of

y\}