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 find the number of applicants who wore neither blue nor white, we can use the principle of inclusion-exclusion. Let: - \( A \) = number of applicants who wore blue = 7 - \( B \) = number of applicants who wore white = 6 - \( C \) = number of applicants who wore both blue and white = 5 The formula to find the total number of applicants who wore either blue or white is: \[ |A \cup B| = |A| + |B| - |C| \] So, \[ |A \cup B| = 7 + 6 - 5 = 8 \] Now we subtract this from the total number of applicants to find those who wore neither color: \[ \text{Applicants who wore neither} = 21 - |A \cup B| = 21 - 8 = 13 \] Therefore, the number of applicants who wore neither blue nor white is **(E) 13**.