Let X-x- x- and -3-x-4 and Y-x- x- and x2-x-6 - 0 - Then the number of elements in X - Y - Y- X is

The correct option is D 4X= {1,2,3} x^2 +x 6 ≤ 0 ⇒ (x+3)(x 2) ≤ 0 ⇒ x ∈ [ 3,2] So, Y={1,2} n(X∩ Y)=2 Hence, n(X × Y) ∩ (Y× X)=(n(X∩ Y))^2 =4 nbsp; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Cartesian Product

Let X=x: x∈ℕ ...

Question

Let $X = {x : x \in N and - 3 < x < 4}$ and $Y = {x : x \in N and x^{2} + x - 6 \leq 0} .$ Then the number of elements in $(X \times Y) \cap (Y \times X)$ is

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $4$
$X = {1, 2, 3}$
$x^{2} + x - 6 \leq 0$
$\Rightarrow (x + 3) (x - 2) \leq 0$
$\Rightarrow x \in [- 3, 2]$
So, $Y = {1, 2}$

$n (X \cap Y) = 2$
Hence, $n (X \times Y) \cap (Y \times X) = (n (X \cap Y))^{2} = 4$

Suggest Corrections

Similar questions

Q. Two sets:

X, Y

such that

X = {x : x \in N; x^{2} - 5 x + 6 = 0} &

B = {1, 2, 5, 3},

then

A \cap B =

Q. Write the following sets in Roster form
(i)

A = {x : x \in N, 2 < X \leq 10}

(ii)

B = {x : x \in Z, - \frac{1}{2} < X < \frac{11}{2}}

(iii)

C =

{

x : x

is a prime number and a divisor of 6 }
(iv)

X =

{

x : x = 2^{n}, n \in N

and

n \leq 5

}
(v)

M = {x : x = 2 y - 1, y \leq 5, y \in W}

(vi)

P =

{

x : x

is an integer,

x^{2} \leq 16

}

Q. Let

P = {x : x \in N and \frac{7}{x + 2} > 1}

and

Q = {x : x \in N and | x - 1 | < 2} .

Then

n (P Δ Q)

Q. Let

A = {x : x \in Z, | x | \leq 3}

and

B = {y; y \in N, - 1 < y + 2 \leq 4}

. If

R

be the relation from

A

B

, then

Q. The cardinal number of the set

Y = {x : x \leq 16 & x \in N}

Join BYJU'S Learning Program

Let X={x:x∈N and −3<x<4} and Y={x:x∈N and x2+x−6≤0}. Then the number of elements in (X×Y)∩(Y×X) is

The correct option is D 4X={1,2,3} x2+x−6≤0 ⇒(x+3)(x−2)≤0 ⇒x∈[−3,2] So, Y={1,2} n(X∩Y)=2 Hence, n(X×Y)∩(Y×X)=(n(X∩Y))2=4

Let $X = {x : x \in N and - 3 < x < 4}$ and $Y = {x : x \in N and x^{2} + x - 6 \leq 0} .$ Then the number of elements in $(X \times Y) \cap (Y \times X)$ is

The correct option is D $4$
$X = {1, 2, 3}$
$x^{2} + x - 6 \leq 0$
$\Rightarrow (x + 3) (x - 2) \leq 0$
$\Rightarrow x \in [- 3, 2]$
So, $Y = {1, 2}$

$n (X \cap Y) = 2$
Hence, $n (X \times Y) \cap (Y \times X) = (n (X \cap Y))^{2} = 4$