If A and B are two sets such that n(A) =20 , n(B) =25 and `n(AcapB)`=5 , then write `n(AuuB)`.

Answer

To find the number of elements in the union of two sets A and B, we can use the formula:

\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]

Where:
- \( n(A) \) is the number of elements in set A
- \( n(B) \) is the number of elements in set B
- \( n(A \cap B) \) is the number of elements in the intersection of sets A and B

Given:
- \( n(A) = 20 \)
- \( n(B) = 25 \)
- \( n(A \cap B) = 5 \)

Now, we can substitute these values into the formula:

1. Calculate \( n(A) + n(B) \):
\[ n(A) + n(B) = 20 + 25 = 45 \]

2. Subtract \( n(A \cap B) \) from the result:
\[ n(A \cup B) = 45 - 5 = 40 \]

Thus, the number of elements in the union of sets A and B is:
\[ n(A \cup B) = 40 \]

**Final Answer:**
\[ n(A \cup B) = 40 \]

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