Let A and B be two stes such that: n(P) = 20, n(A )=42 and n(A )=… - Vidyadip

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: $\text{n(B)}.$

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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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