Question #N656
A survey of 100 people found that 60 people liked apples, 50 people liked oranges, and 20 people liked both apples and oranges. How many people liked neither apples nor oranges?
A. 10
B. 20
C. 30
D. 40
Correct Answer is: C
We can use a Venn Diagram to solve this problem. Let A represent the set of people who like apples and O represent the set of people who like oranges. We are given that |A| = 60, |O| = 50, and |A \cap O| = 20. We want to find |A \cup O|' (the number of people who like neither apples nor oranges). We can use the following formula: |A \cup O| = |A| + |O| - |A \cap O|. Substituting our known values, we get |A \cup O| = 60 + 50 - 20 = 90. Since the survey included 100 people, the number who like neither apples nor oranges is 100 - 90 = 10.