Question

2. (3 pts) A group of 4500 college students were surveyed, and it was found that: 2500 participated in

extracurricular activities 1100 had a double major 1700 had a part-time job 250 both participated in extracurricular activities and had a part-time job 500 both participated in extracurricular activities and had a double major 160 had both a double major and a part-time job 60 participated in extracurricular activities, had a double major, and had a part-time job.

Let A be the set of those students who participated in extracurricular activities, let B be the set of those who had a double major, and let C be the set of those who had a part-time job. Use this information to find the following.

(a) (1 pt) How many students have at least one of the following characteristics: participation in extracurricular activities, having a double major, or having a part-time job?

(b) (1 pt) The set of those students who participated in extracurricular activities, but neither had a double major nor a part time job can be written as A ∩ B’∩ C’. find N(A ∩ B’∩ C’).

(c) (1 pt) How many students had none of the three characteristics, i.e., those who did not participate in extracurricular activities, did not have a double major, and did not have a part time job? answer in set notation and find the number of students. 

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