If n(U)=100,n(A)=30,n(B)=40 and n(Acap B)= 10. Find n(A^{c}cap B^{c}).

Name: If n(U)=100,n(A)=30,n(B)=40 and n(Acap B)= 10. Find n(A^{c}cap B^{c}).
Uploaded: Mon, 2018-12-17 17:16
Description: If n(U)=100,n(A)=30,n(B)=40 and n(Acap B)= 10. Find n(A^{c}cap B^{c}).

How to solve this question? If n(U)=100,n(A)=30,n(B)=40 and n(Acap B)= 10. Find n(A^{c}cap B^{c}).

Answers (2)

The solution to this question can be solved by using the following formula:

$n(U)=100$ $n(A)=30$ $n(B)=40$ $n(A\cap B)=10$
   $n(A^c\cap B^c)=?$
   $(A^c\cap B^c)=(A\cup B)^c$ {De Morgan's Law}

      $n(A\cup B)=n(A)+n(B)-n(A\cap B)$
   $40+30-10=60$
$n(A\cup B)^c=n(U)-n(A\cup B)$
   $=100-60=40$
$n(A\cup B)^c=n(A^c\cap B^c)=40$