Consider the following statements. Let ${A}=\{1,2,3,4\}$ and ${B}=\{5,7,9\}$ I. ${A} \times {B}={B} \times {A}$ II. ${n}({A} \times {B})={n}({B} \times {A})$ Choose the correct option.

JEE MATHEMATICS MCQ: RELATIONS

1 Easy

1 of 1

Understanding +4 | -1

Consider the following statements.

Let

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

and

{B}=\{5,7,9\}

{A} \times {B}={B} \times {A}

II.

{n}({A} \times {B})={n}({B} \times {A})

Choose the correct option.

View answer and explanation

Correct option: B

Statement-II is true

Statement-II is true because the number of elements in the Cartesian product of two sets is the product of the number of elements in each set, regardless of the order of the sets.

More Questions from RELATIONS

Practice All Chapter MCQs →

In the set

\mathrm{Z}

of all integers, which of the following relation

R

is not an equivalence relation? Let

\mathrm{N}

denote the set of all natural numbers and

\mathrm{R}

be the relation on

\mathrm{N} \times \mathrm{N}

defined by

(\mathrm{a}, \mathrm{b}) \mathrm{R}(\mathrm{c}, \mathrm{d})

a d(b+c)=b c(a+d)

, then

\mathrm{R}

is Let

W

denote the words in the English dictionary. Define the relation

R

by:

R=\{(x, y) \in W \times W \mid

the words

x

and

y

have at least one letter in common

\}

Let

S

be the set of all real numbers. Then, the relation

R = \{ \left( {a,\;b} \right):1 + ab > 0\}

S

is Let

X

be a family of sets and

R

be a relation on

X

defined by '

A

is disjoint from

B

'. Then

R

is:

R

is relation on

N

given by

R = \left\{ {\left( {x,\;y} \right):4x + 3y = 20} \right\}

. Which of the following belongs to

R