Let P-x-x- and 7x-2 1 and Q-x- x- and -x-1- 2- Then nP - Q is

7x+2 1 ⇒7x+2 1 gt;0 ⇒5 xx+2 0 ⇒x 5x+2 0 ⇒ x∈ ( 2,5) ∴ P={1,2,3,4} |x 1| 2 ⇒ 2 x 1 2 ⇒ 1 x 3 ∴ Q={1,2} n(P Δ Q)=n(P)+n(Q) 2n(P∩ Q) =4+2 2×2 =2 ...

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

Byju's Answer

Standard XI

Mathematics

Properties of Symmetric Difference of Sets

Let P=x:x∈ℕ a...

Question

Let $P = {x : x \in N and \frac{7}{x + 2} > 1}$ and $Q = {x : x \in N and | x - 1 | < 2} .$ Then $n (P Δ Q)$ is

7

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

8

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

2

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

4

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

Open in App

Solution

The correct option is C $2$
$\frac{7}{x + 2} > 1$
$\Rightarrow \frac{7}{x + 2} - 1 > 0$
$\Rightarrow \frac{5 - x}{x + 2} > 0$
$\Rightarrow \frac{x - 5}{x + 2} < 0$
$\Rightarrow x \in (- 2, 5)$
$∴ P = {1, 2, 3, 4}$

$| x - 1 | < 2$
$\Rightarrow - 2 < x - 1 < 2$
$\Rightarrow - 1 < x < 3$
$∴ Q = {1, 2}$

$n (P Δ Q) = n (P) + n (Q) - 2 n (P \cap Q)$
$= 4 + 2 - 2 \times 2$
$= 2$

Suggest Corrections

Similar questions

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

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)

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. Find

A \cup B

and

A \cap B

for the following sets.
(i)

A = {0, 1, 2, 4, 6}

and

B = {- 3, - 1, 0, 2, 4, 5}

(ii)

A = {2, 4, 6, 8}

and

B = \emptyset

(iii)

A = {x : x \in N, x \leq 5}

and

B =

{

x : x

is a prime number less than 11}
(iv)

A = {x : x \in N, 2 < x \leq 7}

and

B = {x : x \in W, 0 \leq x \leq 6}

Q. Let

A = {x : x \in N and x^{2} - 2 x - 35 < 0}

and

B = {x : x \in Z and 1 < x + 2 < 10} .

Then

n (A Δ B)

Join BYJU'S Learning Program

Let P={x:x∈N and 7x+2>1} and Q={x:x∈N and |x−1|<2}. Then n(PΔQ) is

The correct option is C 27x+2>1 ⇒7x+2−1>0 ⇒5−xx+2>0 ⇒x−5x+2<0 ⇒x∈(−2,5) ∴P={1,2,3,4} |x−1|<2 ⇒−2<x−1<2 ⇒−1<x<3 ∴Q={1,2} n(PΔQ)=n(P)+n(Q)−2n(P∩Q) =4+2−2×2 =2

Let $P = {x : x \in N and \frac{7}{x + 2} > 1}$ and $Q = {x : x \in N and | x - 1 | < 2} .$ Then $n (P Δ Q)$ is