Let n(A−B)=25+x, n(B−A)=2x and n(A∩B)=2x. If n(A)

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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

x

= ___.

Options:

A . 4

B . 5

C . 6

D . 7

Answer: Option B
:
B
Given that

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

and

n (A \cap B) = 2 x .

We know that

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

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

Similarly,

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

= 2 x + 2 x

=

4 x .

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

=

2 \times 4 x

\Rightarrow 5 x = 25 \Rightarrow x = 5

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