Consider the following statements I. Let $n(A)=m$ and $n(B)=n$. Then the total number of non-empty relations that can be defined from $A$ to $B$ is $2^{{mn}}-1$ II. If ${A}=\{1,2,3\}, {B}=\{3,8\}$, then $({A} \cup {B}) \times({A} \cap {B})$ is equal to $\{(1,3),(2,3),(3,3),(8,3)\}.$ III. If $\left(\frac{x}{2}-1, \frac{y}{9}+1\right)=(2,1)$, then the values of ${x}$ and ${y}$ respectively are 6 and 0. Choose the correct option.

JEE MATHEMATICS MCQ: RELATIONS

1 Easy

1 of 1

Understanding +4 | -1

Consider the following statements

I. Let

n(A)=m

and

n(B)=n

. Then the total number of non-empty relations that can be defined from

A

B

2^{{mn}}-1

II. If

{A}=\{1,2,3\}, {B}=\{3,8\}

, then

({A} \cup {B}) \times({A} \cap {B})

is equal to

\{(1,3),(2,3),(3,3),(8,3)\}.

III. If

\left(\frac{x}{2}-1, \frac{y}{9}+1\right)=(2,1)

, then the values of

{x}

and

{y}

respectively are 6 and 0.

Choose the correct option.

View answer and explanation

Correct option: D

All the three statements are true

All three statements are true because they correctly describe the number of relations, the Cartesian product of union and intersection, and the equality of ordered pairs.

JEE MATHEMATICS MCQ: RELATIONS

More Questions from RELATIONS