Question

Let \( U \) be the universal set, \( A \), \( B \), and \( C \) are the sets such that \( C \) is a subset of \( A \) and \( B \cap C = \emptyset \). If \( n(U) = 105 \), \( n(A) = 58 \), \( n(B) = 50 \), \( n(A \cap B) = 20 \) and \( n(A \cap C) = 32 \), then \( n(A \cup B) - n(B \cap C') = ? \)

• A. 58
• B. 59
• C. 60
• D. 65

Hint:

When dealing with set operations, remember that the union of two sets subtracts the intersection, and ensure you handle complements correctly.

Answer 1

The Correct Option is C

To calculate \( n(A \cup B) - n(B \cap C') \), we use the following steps: 1. Find \( n(A \cup B) \): \[ n(A \cup B) = n(A) + n(B) - n(A \cap B) = 58 + 50 - 20 = 88 \] 2. Since \( B \cap C = \emptyset \), \( B \cap C' = B \), so: \[ n(B \cap C') = n(B) = 50 \] 3. Now, calculate \( n(A \cup B) - n(B \cap C') \): \[ 88 - 50 = 60 \] Thus, the final answer is 60.