Question

If \( n(A) = 4 \) and \( n(B) = 7 \), then the difference between the maximum and minimum value of \( n(A \cup B) \) is:

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

The maximum occurs when \( A \cap B = 0 \), and the minimum when \( A \subseteq B \).

Answer 1

The Correct Option is D

Step 1: Using the union formula.
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \] - Maximum value: when \( A \) and \( B \) have no intersection, \[ n(A \cup B) = 4 + 7 = 11. \] - Minimum value: when \( A \) is completely inside \( B \), \[ n(A \cup B) = 7. \] - Difference: \( 11 - 7 = 4 \).