Final answer:
To find the number of students who participated in both swimming and arts and crafts at the summer camp, we can use sets and the inclusion-exclusion principle. First, we find the number of students who signed up for swimming or arts and crafts individually. Then, we subtract the number of students who signed up for both activities.
Step-by-step explanation:
The question is asking how many students participated in both swimming and arts and crafts at the summer camp. To find the answer, we need to use the concept of sets and the inclusion-exclusion principle.
Let's start by finding the number of students who signed up for swimming or arts and crafts individually. We are told that 45 signed up for swimming and 38 signed up for arts and crafts. Adding these two numbers gives us 83.
Next, we need to subtract the number of students who signed up for both swimming and arts and crafts. We are given that 12 students signed up for both activities. Subtracting this from 83 gives us the final answer: 71 students participated in either swimming, arts and crafts, or both.