From a survey of 100 college students, a marketing research company found that 70 students owned iPhones, 45 owned cars, and 40 owned both cars and iPhones.
(a) How many students owned either a car or an iPhone (but not both)?
1 students
(b) How many students do not own either a car or an iPhone?
2 students
To find the answers to the questions, we need to understand the concepts of set theory and use the principle of inclusion-exclusion.
Let's denote the set of students who own iPhones as A, the set of students who own cars as B, and the set of all students as U. We can count the number of students in each set using the given information:
|A| = 70 (students who own iPhones)
|B| = 45 (students who own cars)
|A ∩ B| = 40 (students who own both cars and iPhones)
(a) To find the number of students who own either a car or an iPhone (but not both), we need to subtract the number of students who own both from the total number of students who own either a car or an iPhone.
|A ∪ B| = |A| + |B| - |A ∩ B|
|A ∪ B| = 70 + 45 - 40
|A ∪ B| = 75
Therefore, 75 students own either a car or an iPhone (but not both).
(b) To find the number of students who do not own either a car or an iPhone, we need to subtract the number of students who own either a car or an iPhone from the total number of students.
|U| = 100 (total number of students)
|U - (A ∪ B)| = |U| - |A ∪ B|
|U - (A ∪ B)| = 100 - 75
|U - (A ∪ B)| = 25
Therefore, 25 students do not own either a car or an iPhone.