Question
Let A and B be two stes such that: $\text{n(P)} = 20,$ $\text{n(A}\cup\text{B)=42 and n(A}\cap\text{B})=4.$ Find:
$\text{n(B)}.$

Answer

$\text{n(P)}= 20,\text{ n(A}\cup\text{B) = 42 and n(A}\cap\text{B})=4,$ to find: $\text{n(B)}$
We know $\text{n(A}\cup\text{B) = n(A)+n(B)}-\text{n(A}\cap\text{B})$
$\Rightarrow42 = 20 + \text{n(B)} - 4$
$\Rightarrow42 = 16 + \text{n(B)}$
$\Rightarrow\text{n(B)} = 42 - 16$
$= 26$
$\therefore\text{ n(B)} = 26.$

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