If n ` (A) = 120 ,n (B) = 250 and n (A- B) = 52,` then find n `(A uu B) `

Explanation

To solve the problem, we need to find \( n(A \cup B) \) given the following information:

- \( n(A) = 120 \)
- \( n(B) = 250 \)
- \( n(A - B) = 52 \)

### Step-by-Step Solution:

1. **Understand the relationship between sets**:
We know that \( n(A - B) \) represents the number of elements in set A that are not in set B. This can be expressed using the formula:
\[ n(A - B) = n(A) - n(A \cap B) \]

2. **Set up the equation**:
From the information given, we can set up the equation:
\[ 52 = 120 - n(A \cap B) \]

3. **Solve for \( n(A \cap B) \)**:
Rearranging the equation gives us:
\[ n(A \cap B) = 120 - 52 \]
\[ n(A \cap B) = 68 \]

4. **Use the formula for \( n(A \cup B) \)**:
The formula for the union of two sets is:
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]

5. **Substitute the known values**:
Now we can substitute the values we have:
\[ n(A \cup B) = 120 + 250 - 68 \]

6. **Calculate the result**:
Performing the calculations:
\[ n(A \cup B) = 370 - 68 = 302 \]

Thus, the final answer is:
\[ n(A \cup B) = 302 \]