In a typical semester, MATH1160 would be presented in a lecture hall which can hold around 200 students. Due to the WMU curriculum, the majority of students who take MATH1160 end up being business majors. In the fall semester of 2019, there were 180 students in the 11am lecture of MATH1160. Suppose that 36 of those students were NOT business majors. Further suppose that a total of 28 students got an A in the class, and 122 business majors did not get an A in the class. A. Define the universal set (U) and the minimum number of necessary subsets. (3 points) B. Convert the relevant numerical information in the above paragraph into set theoretic notation. (4 points) C. Create the appropriate Venn diagram and fill in the values associated with each of the basic regions. (4 points) D. How many students in the Fall 2019 11am lecture of MATH1160 either were business majors OR received an A in the class? Write the set theoretical statement corresponding to this question along with your answer. (3 points) E. If a student in the Fall 2019 11 am lecture of MATHI 160 were chosen at random, what is the probability that this student received an A in the class AND was a business major" Write the probability statement corresponding to this question along with your answer. (3 points)