Let U be the universal set containing 700 elements. If A, B are sub-sets of U such that
\[ n(A)=200,\quad n(B)=300,\quad n(A\cap B)=100 \]
Then,
\[ n(A’ \cap B’)= \]
(a) 400
(b) 600
(c) 300
(d) none of these
Solution
Using De Morgan’s law,
\[ A’\cap B’=(A\cup B)’ \]
Therefore,
\[ n(A’\cap B’)=n(U)-n(A\cup B) \]
Now,
\[ n(A\cup B)=n(A)+n(B)-n(A\cap B) \]
\[ =200+300-100 \]
\[ =400 \]
Hence,
\[ n(A’\cap B’)=700-400 \]
\[ =300 \]
Answer
\[ \boxed{300} \]
Correct option: (c)