Question

A is the set of students at Winfield College who had a 4.0 GPA for the fall 2012 semester. B is the set of students at Winfield College who had a 4.0 GPA for the spring 2013 semester.

(a) Describe A∩B.
(b) Is A a subset of B?
(c) Describe A∪B.

A) (a) 4.0 GPA students in both semesters, (b) Yes, (c) 4.0 GPA students in either semester.
B) (a) All students in both semesters, (b) No, (c) All students in either semester.
C) (a) 4.0 GPA students in either semester, (b) Yes, (c) 4.0 GPA students in both semesters.
D) (a) All students in either semester, (b) No, (c) All students in both semesters.

Answer 1

A∩B represents students with a 4.0 GPA in both semesters, A is not necessarily a subset of B, and A∪B includes 4.0 GPA students from either semester. The correct answer is option A.

Step-by-step explanation:

The student's question touches on the concepts of set theory, specifically intersections, unions, and subsets. For part (a), A∩B (the intersection of sets A and B) is the set containing all students at Winfield College who had a 4.0 GPA in both the fall 2012 semester and the spring 2013 semester. For part (b), A is not necessarily a subset of B, as we don't have enough information to conclude that every student with a 4.0 GPA in the fall also had a 4.0 GPA in the spring. Lastly, for part (c), A∪B (the union of sets A and B) represents all students who had a 4.0 GPA in either semester, which includes students who had a 4.0 in just one semester as well as those who had a 4.0 in both semesters. Based on these explanations, the correct answer is option A: (a) 4.0 GPA students in both semesters, (b) Yes, (c) 4.0 GPA students in either semester.