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Question

$$n\left( A \right) =50, n\left( B \right) =20$$ and $$n\left( A\cap B \right) =10$$, then $$n\left( A\triangle B \right) $$ is


A
50
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B
60
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C
70
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D
40
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Solution

The correct option is B $$50$$
$$\mathrm{n}(\mathrm{A}\Delta \mathrm{B})=\mathrm{n} (\mathrm{A} \cup \mathrm{B})-\mathrm{n} (\mathrm{A} \cap \mathrm{B})$$      [As $$n(A\cup B) = n(A)+ n(B) - n(A \cap B )$$]
$$=\mathrm{n}(\mathrm{A})+\mathrm{n}(\mathrm{B})-2\mathrm{n} (\mathrm{A} \cap\mathrm{B})$$
$$=50+20-2(10)=50$$

Mathematics

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