Beta Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>EXERCISE-1>Q 33

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If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements, then the number of relations from $A$ to $B$ is-

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Important Questions on Set Theory and Relations

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Beta Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>EXERCISE-1>Q 34

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

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Beta Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>EXERCISE-1>Q 35

For real numbers

x

and

y

, we write

x R y \Leftrightarrow x - y + \sqrt{2}

is an irrational number. Then, the relation

R

is

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Beta Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>EXERCISE-1>Q 36

Let

X = \{1, 2, 3, 4, 5\}

and

Y = \{1, 3, 5, 7, 9\}

. Which of the following is relations from

X

to

Y

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Beta Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>EXERCISE-1>Q 37

Let

L

denote the set of all straight lines in a plane. Let a relation

R

be defined by

α R β \Leftrightarrow α ⊥ β

,

α, β \in L

. Then

R

is

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Beta Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>EXERCISE-1>Q 38

Let

R

be a relation defined in the set of real numbers by

a R b \Leftrightarrow 1 + a b > 0

. Then

R

is

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Beta Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>EXERCISE-1>Q 39

Which one of the following relations on

R

is equivalence relation

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Beta Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>EXERCISE-1>Q 40

Two points

P

and

Q

in a plane are related if

O P = O Q

, where

O

is a fixed point. This relation is

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Beta Question Bank for Engineering: Mathematics>Chapter 2 - Set Theory and Relations>EXERCISE-1>Q 41

The relation

R

defined in

A = \{1, 2, 3\}

by

a R b

if

|a^{2} - b^{2}| \leq 5

. Which of the following is false-