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

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Answer

To find: $\text{B}- \text{A}$ On a similar lines we have B is the disjoint union of $\text{B} - \text{A}$ and $\text{A}\cap\text{B}$ i.e., $\text{B = (B} - \text{A)}\cup\text{(A}\cap\text{B})$ $\therefore\text{ n(B)=n(B}- \text{A)}+\text{n}\text{(A}\cap\text{B})$ $\Rightarrow26 = \text{n(B} - \text{A)} + 4$ $\Rightarrow\text{n(B} - \text{A)} = 26 - 4$ $= 22$ $\therefore\text{n(B} - \text{A)} = 22.$

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