Question

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 1

Answer:80students

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.