Et P - x - x - N- and -7- x -2-1 and Q - x - x - N and - x -1-2 - Then n P - Q isA- 2B- 4C- 7D- 8

The correct option is A 27x+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( ...

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Byju's Answer

Standard XII

Mathematics

Difference of Two Sets

et P = x : x ...

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

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Solution

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

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

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

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Similar questions

Q. Let

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

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If P = ${x : x \in W a n d 4 \leq x \leq 8}$ , and Q = ${x : x \in N a n d x < 6}$ . Find : (i) $P \cup Q$ and $P \cap Q$ (ii) Is $(P \cup Q) \supset (P \cap Q)$

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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