Question

If n (A) = 20, n (B) = 28 and n( A U B) = 36 then n (A n B) = ?

Answer 1

GIVEN :

If n (A) = 20, n (B) = 28 and $n( A\cup B) = 36$ then $n (A\cap B)$

TO FIND :

The value of  $n (A\cap B)$

SOLUTION :

Given that n (A) = 20, n (B) = 28 and $n( A\cup B) = 36$

The formula in Set theory is given by :

$n( A\cup B) = n(A)+n(B)-n (A\cap B)$

Now substituting the values in the above formula we get,

$36 = 20+28-n (A\cap B)$

$36=48-n (A\cap B)$

$n (A\cap B)=48-36$

= 12

∴ $n (A\cap B)=12$

∴ the value of $n (A\cap B)$ is 12

Answer 2

Answer:

n(A∪B)=n(A)+n(B)−n(A∩B)

:36=20+28-n(A∩B)

:36=48-(A∩B)

:A∩B)=48-36=12