In the set A-1- 2- 3- 4- 5- a relation R is defined by R-x- y-x- y- A and x-y- Then R is

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Standard XII

Mathematics

Definition of Relations

In the set ...

Question

In the set $A = {1, 2, 3, 4, 5}$ , a relation $R$ is defined by
$R = {(x, y) : x, y \in A$ and $x < y}$ . Then $R$ is

reflexive

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symmetric

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transitive

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None of these

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Solution

The correct option is C transitive

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Q. 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 ): 3 x − 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} (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 }

Q. In the set

A = {1, 2, 3, 4, 5}

, a relation

R

is defined by

R = {(x, y) | x, y \in A a n d x < y}

. Then

R

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}

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

(d) R = {(x, y): x is wife of y}

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

Q. The relation

R

defined on the set

A = {1, 2, 3, 4, 5}

R = {(x, y) : | x^{2} - y^{2} | < 16}

is given by

Q. If the relation

R : A \to B

where

A = {1, 2, 3, 4}, B = {1, 3, 5}

is defined by

R = {(x, y) : x < y, x \in A, y \in B}

then find

R

and

R^{- 1}

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In the set A={1,2,3,4,5}, a relation R is defined byR={(x,y):x,y∈A and x<y}. Then R is

The correct option is C transitive

In the set $A = {1, 2, 3, 4, 5}$ , a relation $R$ is defined by
$R = {(x, y) : x, y \in A$ and $x < y}$ . Then $R$ is