Let n A - B -25- x - n B - A -2 x and n A - B -2 x- If n A -2 n B then the value of -x-is the

N (A B) = 25 + x,n(B A) = 2x n(A∩ B) = 2x n(A) = n(A B)+n(A∩ B) = 25 + x +2x = 25 + 3x n(B) = n(B A) + n(A ∩ B) = 2x + 2x = 4x n(A) = 2n(B) ⇒ 25 + 3x = ...

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Byju's Answer

Standard IX

Mathematics

Distributive Property

Let n A - B =...

Question

Let $n (A - B)$ = $25 + x$ , $n (B - A)$ = $2 x$ and $n (A \cap B)$ = $2 x$ . If n(A) = 2(n(B)) then the value of 'x' is ___.

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Solution

$n (A - B) = 25 + x, n (B - A) = 2 x$

$n (A \cap B) = 2 x$

$n (A) = n (A - B) + n (A \cap B)$

$= 25 + x + 2 x = 25 + 3 x$

$n (B) = n (B - A) + n (A \cap B)$
$= 2 x + 2 x = 4 x$

$n (A) = 2 n (B) \Rightarrow 25 + 3 x$
$= 2 (4 x)$

$\Rightarrow 5 x = 25 \Rightarrow x = 5$

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Let n(A−B) = 25+x, n(B−A) = 2x and n(A∩B) = 2x. If n(A) = 2(n(B)) then the value of 'x' is ___.

n(A−B)=25+x,n(B−A)=2x n(A∩B)=2x n(A)=n(A−B)+n(A∩B) =25+x+2x=25+3x n(B)=n(B−A)+n(A∩B) =2x+2x=4x n(A)=2n(B)⇒25+3x =2(4x) ⇒5x=25⇒x=5

Let $n (A - B)$ = $25 + x$ , $n (B - A)$ = $2 x$ and $n (A \cap B)$ = $2 x$ . If n(A) = 2(n(B)) then the value of 'x' is ___.

$n (A - B) = 25 + x, n (B - A) = 2 x$

$n (A \cap B) = 2 x$

$n (A) = n (A - B) + n (A \cap B)$

$= 25 + x + 2 x = 25 + 3 x$

$n (B) = n (B - A) + n (A \cap B)$
$= 2 x + 2 x = 4 x$

$n (A) = 2 n (B) \Rightarrow 25 + 3 x$
$= 2 (4 x)$

$\Rightarrow 5 x = 25 \Rightarrow x = 5$