Question

Let $n ( U ) = 700 , n ( A ) = 200 , n ( B ) = 300$ and $n ( A \cap B ) = 100$ then $n \left( A ^ { c } \cap B ^ { c } \right) =$

• A. 400
• B. 600
• C. 300
• D. 200

Answer 1

Answer: (C)

300

Answer 2

$n \left( A ^ { c } \cap B ^ { c } \right)$ = n[(A ∪ B)^c] = $n ( U ) - n ( A \cup B )$

= $n ( U ) - [ n ( A ) + n ( B ) - n ( A \cap B ) ]$ = 700 – [200 + 300 – 100]

= 300.