23. A company interviewed 21 applicants for a recent opening. Of these applicants, 7 wore blue and 6 wore white, while 5 applicants wore both blue and white. What is the number of applicants who wore neither blue nor white? (A) 1 (B) 6 (C) 8 (D) 12 (E) 13

To determine the number of applicants who wore neither blue nor white, we can use the principle of inclusion-exclusion. 1. **Total number of applicants:** 21 2. **Applicants who wore blue (B):** 7 3. **Applicants who wore white (W):** 6 4. **Applicants who wore both blue and white (B ∩ W):** 5 First, calculate the number of applicants who wore either blue or white (or both): \[ |B \cup W| = |B| + |W| - |B \cap W| = 7 + 6 - 5 = 8 \] Now, subtract this from the total number of applicants to find those who wore neither color: \[ \text{Applicants who wore neither} = 21 - 8 = 13 \] **Answer:** (E) 13