Q76 / 180 · KCET 2019 · Mathematics

If $ U $ is the universal set with $ 100 $ elements; $ A $ and $ B $ are two sets such that $ n(A)=50, n(B)=60 $,
$ n(A \cap B)=20 $ then $ n\left(A^{\prime} \cap B^{\prime}\right)= $

A
$ 20 $
Correct answer
B
$ 10 $
C
$ 40 $
D
$ 90 $

Solution

$(B)$ $n(U)=100$ $n(A)=50$ $n(B)=60$ $n(A \cap B)=20$ $n(A \cup B)=n(A)+n(B)-n(A \cap B)$ $=50+60-20$ $=110-20$ $=90$ $n\left(A^{\prime} \cap B^{\prime}\right)=n(A \cup B)^{\prime}$ $=n(U)-n(A \cup B)$ $=100-90$ $=10$

Hence, the correct answer is option: 'B'.

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If \( U \) is the universal set with \( 100 \) elements; \( A \) and \( B \) are two sets such that \( n(A)=50, n(B)=60 \),\( n(A \cap B)=20 \) then \( n\left(A^{\prime} \cap B^{\prime}\right)= \)

Solution

Relevant Questions

If \( U \) is the universal set with \( 100 \) elements; \( A \) and \( B \) are two sets such that \( n(A)=50, n(B)=60 \),
\( n(A \cap B)=20 \) then \( n\left(A^{\prime} \cap B^{\prime}\right)= \)