Question

A and B are two sets such that \( n(A) = 12 \), \( n(B) = 15 \) and \( n(A \cup B) = 20 \). Then, \( n(B \cap A') - n(A \cap B') = ?

• A. 5
• B. 4
• C. 3
• D. 2

Hint:

For set operations, use the inclusion-exclusion principle to calculate intersections and differences.

Answer 1

The Correct Option is A

We are given: - \( n(A) = 12 \) - \( n(B) = 15 \) - \( n(A \cup B) = 20 \) From the formula for the union of two sets, we know: \[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \] Substitute the known values: \[ 20 = 12 + 15 - n(A \cap B) \] \[ n(A \cap B) = 7 \] Calculate \( n(B \cap A') \) The number of elements in \( B \) but not in \( A \) is: \[ n(B \cap A') = n(B) - n(A \cap B) = 15 - 7 = 8 \] Calculate \( n(A \cap B') \) The number of elements in \( A \) but not in \( B \) is: \[ n(A \cap B') = n(A) - n(A \cap B) = 12 - 7 = 5 \] Final calculation Now, we calculate: \[ n(B \cap A') - n(A \cap B') = 8 - 5 = 3 \] Thus, the answer is \( 5 \).