Question

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

• A. 58
• B. 60
• C. 78
• D. 88

Hint:

Use the formula \( n(A \cup B) = n(A) + n(B) - n(A \cap B) \) for union operations quickly.

Answer 1

The Correct Option is D

We are given: \[ n(A \cup B) = n(A) + n(B) - n(A \cap B) = 58 + 50 - 20 = 88 \] Since \( B \cap C = \emptyset \), we have: \[ n(B \cap C) = 0 \Rightarrow n(A \cup B) - n(B \cap C) = 88 - 0 = 88 \]