Question
30 students play cricket, and 20 play football. If 10 play both, how many play at least one sport?
Answers
GPT-4o mini
To solve this problem, we can use the principle of inclusion-exclusion.
Let's define:
- \( A \) = the set of students who play cricket
- \( B \) = the set of students who play football
According to the problem:
- \( |A| = 30 \) (the number of students who play cricket)
- \( |B| = 20 \) (the number of students who play football)
- \( |A \cap B| = 10 \) (the number of students who play both cricket and football)
We want to find the number of students who play at least one sport, which is represented by the union of sets \( A \) and \( B \):
\[
|A \cup B| = |A| + |B| - |A \cap B|
\]
Plugging in the values we have:
\[
|A \cup B| = 30 + 20 - 10 = 40
\]
Therefore, the total number of students who play at least one sport is \( \boxed{40} \).
Let's define:
- \( A \) = the set of students who play cricket
- \( B \) = the set of students who play football
According to the problem:
- \( |A| = 30 \) (the number of students who play cricket)
- \( |B| = 20 \) (the number of students who play football)
- \( |A \cap B| = 10 \) (the number of students who play both cricket and football)
We want to find the number of students who play at least one sport, which is represented by the union of sets \( A \) and \( B \):
\[
|A \cup B| = |A| + |B| - |A \cap B|
\]
Plugging in the values we have:
\[
|A \cup B| = 30 + 20 - 10 = 40
\]
Therefore, the total number of students who play at least one sport is \( \boxed{40} \).