https://file.aiquickdraw.com/mathbot/file/17273654893586q1gme5q.jpg

The problem provided is as follows:

**Problem:**
There are 200 students in a school, 130 students participate in the PMR extracurricular, and 120 students participate in the theater extracurricular. Let \( p \) be the minimum number of students who participate in both extracurricular activities, and \( q \) be the maximum number of students who participate in both. What is the difference between \( p \) and \( q \)?

**Solution:**

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

### Step 1: Maximum overlap (\( q \))

The maximum number of students who can participate in both extracurriculars happens when the number of students in both sets (PMR and theater) is as large as possible. This is limited by the smaller of the two groups, which means:
\[
q = \min(130, 120) = 120
\]

### Step 2: Minimum overlap (\( p \))

The minimum number of students participating in both extracurriculars occurs when as many students as possible are only in one of the two activities. We know the total number of students is 200. The number of students participating in only one of the activities is given by:
\[
p = 130 + 120 - 200 = 50
\]
Thus, the minimum number of students in both extracurriculars is \( p = 50 \).

### Step 3: Difference between \( p \) and \( q \)

Finally, the difference between \( p \) and \( q \) is:
\[
q - p = 120 - 50 = 70
\]

So, the correct answer is **B. 70**.

Let me know if you need further details or explanations. Here are 5 related questions for further practice:

1. If the total number of students was 250, and the groups were 130 and 120, what would \( p \) and \( q \) be?
2. How would you calculate the minimum overlap if the total number of students was unknown?
3. If 90 students participated in both activities, how many participated in only one of the activities?
4. How would the problem change if three extracurricular activities were involved?
5. What if the numbers of participants in PMR and theater were reversed?

**Tip:** To solve problems involving groups and overlaps, always think about maximum and minimum possibilities using the principle of inclusion-exclusion.

Ada 200 siswa di suatu sekolah, 130 siswa mengikuti ekstrakurikuler PMR, 120 siswa mengikuti ekstrakurikuler teater. Jika p adalah jumlah minimum siswa yang mengikuti keduanya dan q adalah jumlah maksimum siswa yang mengikuti keduanya. Maka selisih p dan q adalah?

Pelajari cara menghitung selisih antara jumlah minimum dan maksimum siswa yang mengikuti dua ekstrakurikuler menggunakan prinsip inklusi-eksklusi. Contoh ini menggunakan 200 siswa, dengan 130 siswa mengikuti PMR dan 120 siswa mengikuti teater.

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