Single Choice

If $$A$$ and $$B$$ are subsets of $$U$$ such that $$n(U) = 700, n(A) = 200, n(B) = 300, n$$$$\displaystyle \left ( A\cap B \right )$$ $$= 100$$, then find $$n\displaystyle \left ( A'\cap B' \right )$$

A$$405$$
B$$305$$
C$$400$$
D$$300$$
Correct Answer

Solution

We know that $$\displaystyle \left ( A\cup B \right )'=$$ $$\displaystyle A'\cap B'$$ so we need to find $$\displaystyle \left ( A\cup B \right ) $$ first.
$$n\displaystyle \left ( A\cup B \right ) =$$ $$n(A) + n(B) - n$$\displaystyle (A\cap B)$$ $$= 200 + 300 - 100 = 400$$
$$n\displaystyle \left ( A\cup B \right )' =$$ $$n(U) - n$$\displaystyle \left ( A\cup B \right )'=$$ 700 - 400 = 300$$
$$\displaystyle \Rightarrow $$ $$n\displaystyle (A'\cap B')$$= 300$$.

SIMILAR QUESTIONS

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