Question

A survey of students at Gulf Coast State College who were involved in campus clubs showed that 26 students belonged to the African American Student Union (AASU), 35 students belonged the Student Government Association (SGA), and 12 students belonged to both clubs. How many students in this survey belonged to either the AASU or the SGA? Use the cardinal number formula: n(A∪B)=n(A)+n(B)−n(A∩B)

Answer 1

By applying the cardinal number formula to the given data, it is determined that 49 students at Gulf Coast State College belonged to either the African American Student Union (AASU) or the Student Government Association (SGA).

Step-by-step explanation:

To determine how many students at Gulf Coast State College belonged to either the African American Student Union (AASU) or the Student Government Association (SGA), we can use the cardinal number formula for the union of two sets: n(A∪B) = n(A) + n(B) − n(A∩B). The term n(A∪B) represents the number of students in at least one of the clubs, n(A) represents the number of students in the AASU, n(B) represents the number of students in the SGA, and n(A∩B) represents the number of students in both clubs.

According to the given numbers:

n(A) = 26 students in AASU

n(B) = 35 students in SGA

n(A∩B) = 12 students in both AASU and SGA

Using the formula, we calculate:

n(A∪B) = n(A) + n(B) − n(A∩B)

n(A∪B) = 26 + 35 − 12

n(A∪B) = 61 - 12

n(A∪B) = 49

Therefore, there are 49 students at Gulf Coast State College who belonged to either the AASU or the SGA.