At a graduation ceremony, some students earned bachelors in science degrees, some earned bachelors in arts degrees, and some students double-majored and earned both degrees. If 200 students in total received bachelors degrees in the arts and sciences, how many students earned bachelors in science degrees? a. 120 students earned only a bachelors in arts. b. 40 students earned only a bachelors in science.

Answer:80students

Step-by-step explanation:

Using set notation concept,

n (U) be the total number of student = 200

n (AnS') be those that earned Bachelor in Art only = 120

n (A'nS) be those that earned Bachelor in Science only = 40

n (AnS) be students that earned both degrees.

Using the formulae below to calculate n (AnS) first;

n (AuS) = n (A'nS) + n (AnS) + n (AnS')

200=40+n (AnS) + 120

200=160+n (AnS)

n (AnS) = 40

This shows that 40students earned bachelor in both degrees

Those that earned Bachelor in science degree will then be n (A'nS) + n (AnS) i. e 40+40 = 80students.

NB: A' means complement of A (A not included)

'n' denote intersection and 'u' denote union.