Score: \( 8.5 / 100 \) Question 3 A group of 335 students were surveyed about the courses they were taking at their college with the following results: 209 students said they were taking Math. 120 students said they were taking English. 181 students said they were taking History. 47 students said they were taking Math and English. 105 students said they were taking Math and History. 77 students said they were taking English and Hirtory. 23 students said they were taking all three courses. Make a Venn diagram to illustrate this situation How many students took English and History, but not Math? Question Help: Vint Submit Question

To solve this problem, we need to use the given information to create a Venn diagram and then determine how many students took English and History but not Math. Let's denote: - M as the number of students taking Math - E as the number of students taking English - H as the number of students taking History From the information given: - M = 209 - E = 120 - H = 181 - M ∩ E = 47 (students taking both Math and English) - M ∩ H = 105 (students taking both Math and History) - E ∩ H = 77 (students taking both English and History) - M ∩ E ∩ H = 23 (students taking all three courses) We want to find the number of students who took English and History but not Math, which is E ∩ H - (M ∩ E ∩ H). Let's calculate it step by step: 1. E ∩ H = 77 (students taking both English and History) 2. M ∩ E ∩ H = 23 (students taking all three courses) Now, subtract the students who took all three courses from the students who took English and History to find those who took only English and History: E ∩ H - (M ∩ E ∩ H) = 77 - 23 = 54 So, 54 students took English and History but not Math.