(B) The number of elements common to $A \times B$ and $B \times A$ is given by $n((A \times B) \cap (B \times A))$.Using the property of Cartesian pro

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) The number of elements common to $A \times B$ and $B \times A$ is given by $n((A \times B) \cap (B \times A))$.Using the property of Cartesian products,$(A \times B) \cap (B \times A) = (A \cap B) \times (B \cap A)$.Therefore,$n((A \times B) \cap (B \times A)) = n((A \cap B) \times (A \cap B)) = n(A \cap B) \times n(A \cap B)$.Given that $n(A \cap B) = 99$,we have $99 \times 99 = 99^2$.

Class 11 Mathematics Relations and Functions Cartesian Products of Sets

Difficult

If two sets $A$ and $B$ have $99$ elements in common,then the number of elements common to each of the sets $A \times B$ and $B \times A$ is

A
$2^{99}$
B
$99^2$
C
$100$
D
$18$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Relations and Functions

Subtopic

Cartesian Products of Sets

If $A \times B = \{(p, q), (p, r), (m, q), (m, r)\}$,find $A$ and $B$.

Easy

View Solution

Suppose that the number of elements in set $A$ is $p$,the number of elements in set $B$ is $q$ and the number of elements in $A \times B$ is $7$,then $p^2+q^2=$

EasyKCET 2022

View Solution

If $P = \{a, b, c\}$ and $Q = \{r\}$,find the sets $P \times Q$ and $Q \times P$. Are these two products equal?

Easy

View Solution

Let $A = \{1, 2, 3\}$,$B = \{3, 4\}$,and $C = \{4, 5, 6\}$. Find $A \times (B \cap C)$.

Easy

View Solution

Let $A = \{1, 2, 3\}$,$B = \{3, 4\}$ and $C = \{4, 5, 6\}$. Find $(A \times B) \cup (A \times C)$.

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If two sets $A$ and $B$ have $99$ elements in common,then the number of elements common to each of the sets $A \times B$ and $B \times A$ is

Similar Questions

If $A \times B = \{(p, q), (p, r), (m, q), (m, r)\}$,find $A$ and $B$.

Suppose that the number of elements in set $A$ is $p$,the number of elements in set $B$ is $q$ and the number of elements in $A \times B$ is $7$,then $p^2+q^2=$

If $P = \{a, b, c\}$ and $Q = \{r\}$,find the sets $P \times Q$ and $Q \times P$. Are these two products equal?

Let $A = \{1, 2, 3\}$,$B = \{3, 4\}$,and $C = \{4, 5, 6\}$. Find $A \times (B \cap C)$.

Let $A = \{1, 2, 3\}$,$B = \{3, 4\}$ and $C = \{4, 5, 6\}$. Find $(A \times B) \cup (A \times C)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module