If n(A) = 20, n(B) = 28, and `n(AuuB)=36`, then find `n(AnnB)`.

Answer

To find the number of elements in the intersection of sets A and B (denoted as n(A ∩ B)), we can use the formula for the union of two sets:

\[ n(A ∪ B) = n(A) + n(B) - n(A ∩ B) \]

Given:
- n(A) = 20
- n(B) = 28
- n(A ∪ B) = 36

We can substitute these values into the formula:

1. Write the formula:
\[ n(A ∪ B) = n(A) + n(B) - n(A ∩ B) \]

2. Substitute the known values:
\[ 36 = 20 + 28 - n(A ∩ B) \]

3. Calculate the sum of n(A) and n(B):
\[ 36 = 48 - n(A ∩ B) \]

4. Rearrange the equation to solve for n(A ∩ B):
\[ n(A ∩ B) = 48 - 36 \]

5. Perform the subtraction:
\[ n(A ∩ B) = 12 \]

Thus, the number of elements in the intersection of sets A and B is:
\[ n(A ∩ B) = 12 \]