Let A-x-x- and x2 -2x-35 0 and B -x- x - and 1 x-2 10- Then n A - B is

X^2 2x 35 0 ⇒ (x+5)(x 7) 0 ⇒ x∈ ( 5,7) So, A= {1,2,3,4,5,6} n(A)=6 1 x+2 10 ⇒ 1 x 8 So, B= {0,1,2,3,4,5,6,7} n(B)=8 n(A Δ B) =n(A)+ n(B) 2 n(A ∩ B) =6 ...

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Byju's Answer

Standard XIII

Mathematics

Properties of Symmetric Difference of Sets

Let A=x:x∈ℕ a...

Question

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 $n (A Δ B)$ is

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Solution

The correct option is B $2$
$x^{2} - 2 x - 35 < 0$
$\Rightarrow (x + 5) (x - 7) < 0$
$\Rightarrow x \in (- 5, 7)$
So, $A = {1, 2, 3, 4, 5, 6}$
$n (A) = 6$

$1 < x + 2 < 10$
$\Rightarrow - 1 < x < 8$
So, $B = {0, 1, 2, 3, 4, 5, 6, 7}$
$n (B) = 8$

$n (A Δ B) = n (A) + n (B) - 2 n (A \cap B)$
$= 6 + 8 - 2 \times 6$
$= 2$

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Let A={x:x∈N and x2−2x−35<0} and B={x:x∈Z and 1<x+2<10}. Then n(AΔB) is

The correct option is B 2 x2−2x−35<0 ⇒(x+5)(x−7)<0 ⇒x∈(−5,7) So, A={1,2,3,4,5,6} n(A)=6 1<x+2<10 ⇒−1<x<8 So, B={0,1,2,3,4,5,6,7} n(B)=8 n(AΔB)=n(A)+n(B)−2n(A∩B) =6+8−2×6 =2

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 $n (A Δ B)$ is