X and Y are disjoint sets , If n (X) = 40 and n(Y) = 28 , then find `n(X-Y) +n(Y-X)`.

Answer

To solve the problem, we need to find the value of \( n(X - Y) + n(Y - X) \) given that \( n(X) = 40 \) and \( n(Y) = 28 \), and that sets \( X \) and \( Y \) are disjoint.

### Step-by-Step Solution:

1. **Understanding Disjoint Sets**:
- Since \( X \) and \( Y \) are disjoint sets, it means they have no elements in common. Therefore, the intersection of sets \( X \) and \( Y \) is empty.
- Mathematically, this can be expressed as \( n(X \cap Y) = 0 \).

2. **Finding \( n(X - Y) \)**:
- The expression \( n(X - Y) \) represents the number of elements in set \( X \) that are not in set \( Y \).
- Since \( X \) and \( Y \) are disjoint, all elements of \( X \) are not in \( Y \).
- Therefore, \( n(X - Y) = n(X) = 40 \).

3. **Finding \( n(Y - X) \)**:
- The expression \( n(Y - X) \) represents the number of elements in set \( Y \) that are not in set \( X \).
- Similarly, since \( X \) and \( Y \) are disjoint, all elements of \( Y \) are not in \( X \).
- Therefore, \( n(Y - X) = n(Y) = 28 \).

4. **Calculating \( n(X - Y) + n(Y - X) \)**:
- Now, we can add the two results together:
\[ n(X - Y) + n(Y - X) = n(X) + n(Y) = 40 + 28 = 68 \]

5. **Final Answer**:
- Thus, the final answer is:
\[ n(X - Y) + n(Y - X) = 68 \]