In a class of 30 students, 18 take Mathematics, 5 take both Mathematics an Biology and 8 take neither Mathematics nor Biology. Find the number of students that take Biology? \( \begin{array}{ll}\text { A) } 6 & \text { B) } 8 \\ \text { C) } 13 & \text { D) } 9\end{array} \)

To solve the problem, we first determine how many students take at least one of the subjects: Mathematics or Biology. Since there are 30 students in total and 8 take neither subject, we have: \[ 30 - 8 = 22 \quad \text{(students taking at least one subject)} \] Let \( M \) represent the number of students taking Mathematics, \( B \) represent those taking Biology, and \( x \) be the number of students taking both subjects. From the information provided, we know: - \( M = 18 \) - \( x = 5 \) (students taking both subjects) We can use the principle of inclusion-exclusion to find the number of students taking only Biology: \[ B = \text{Total} - M + x \] Substituting the values we have: \[ B = 22 - 18 + 5 = 9 \] Therefore, the number of students that take Biology is \( \text{D) } 9\).