Question

Of the students in Amy's class, 7 have seen a starfish. 7 students have seen a jellyfish. 2 students have seen both a starfish and a jellyfish. How many students have seen a starfish or a jellyfish or both?

Hint: Use a Venn diagram to help you solve the problem.

students

Answer 1

To solve the problem, we can use the principle of inclusion-exclusion.

Let:
- \( A \) be the set of students who have seen a starfish.
- \( B \) be the set of students who have seen a jellyfish.

From the information given:
- \( |A| = 7 \) (the number of students who have seen a starfish)
- \( |B| = 7 \) (the number of students who have seen a jellyfish)
- \( |A \cap B| = 2 \) (the number of students who have seen both a starfish and a jellyfish)

We want to find the number of students who have seen either a starfish or a jellyfish or both, denoted as \( |A \cup B| \).

Using the formula for the union of two sets:
\[
|A \cup B| = |A| + |B| - |A \cap B|
\]

Substituting the values we have:
\[
|A \cup B| = 7 + 7 - 2
\]
\[
|A \cup B| = 14 - 2
\]
\[
|A \cup B| = 12
\]

Thus, the number of students who have seen a starfish or a jellyfish or both is **12 students**.