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

Step 1: Define the sets

• Let $S$ be the set of students who play soccer.
• Let $B$ be the set of students who play basketball.

Step 2: Given values

• $|S| = 18$ (students who play soccer)
• $|B| = 15$ (students who play basketball)
• $|S \cap B| = 5$ (students who play both soccer and basketball)

Step 3: Apply the principle of inclusion-exclusion

The number of students who play either soccer, basketball, or both is given by the formula:

$|S \cup B| = |S| + |B| - |S \cap B|$

Step 4: Substitute the given values into the formula

$|S \cup B| = 18 + 15 - 5 = 28$

Conclusion:

There are 28 students who play either soccer or basketball or both.

Would you like further details or have any questions?

---

Here are 5 related questions:

1. How many students play only soccer?
2. How many students play only basketball?
3. How many students do not play either soccer or basketball?
4. If 7 additional students start playing soccer, how would that affect the total?
5. What is the probability that a randomly chosen student plays both sports?

Tip: When working with sets and overlapping groups, always consider the principle of inclusion-exclusion to avoid double-counting.