JEE MATHEMATICS MCQ: RELATIONS

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Understanding +4 | -1

Consider the following statements.

I. If the set

{A}

has 3 elements and set

{B}=\{3,4,5\}

, then the number of elements in

{A} \times {B}=9

.

II. The domain of the relation

{R}

defined by

{R}=\{({x}, {x}+5): {x} \in(0,1,2,3,4,5)\} \text { is }\{5,6,7,8,9,10\} .

Choose the correct option.

View answer and explanation

Correct option: A

Only I is true

Only I is true because the number of elements in the Cartesian product is the product of the number of elements in each set, while the domain in statement II is incorrectly calculated.

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