Make a problem using Venn diagram with 2 circle and solution 

### Problem:
In a class of 50 students:
- 30 students study Mathematics.
- 25 students study Science.
- 10 students study both Mathematics and Science.

How many students:
1. Study only Mathematics?
2. Study only Science?
3. Study either Mathematics or Science?
4. Study neither Mathematics nor Science?

Use a Venn Diagram with two circles to represent this data and solve the questions.

---

### Solution:

Let's define:
- \( M \): The set of students who study Mathematics.
- \( S \): The set of students who study Science.
- \( M \cap S \): The set of students who study both subjects.

From the problem:
- Total students = 50
- \( |M| = 30 \)
- \( |S| = 25 \)
- \( |M \cap S| = 10 \)

#### Step 1: Finding Students in Each Category

1. **Students who study only Mathematics**:  
   This group includes students in \( M \) but not in \( S \).
   \[
   |M \text{ only}| = |M| - |M \cap S| = 30 - 10 = 20
   \]

2. **Students who study only Science**:  
   This group includes students in \( S \) but not in \( M \).
   \[
   |S \text{ only}| = |S| - |M \cap S| = 25 - 10 = 15
   \]

3. **Students who study either Mathematics or Science**:  
   This includes students in \( M \cup S \).
   \[
   |M \cup S| = |M| + |S| - |M \cap S| = 30 + 25 - 10 = 45
   \]

4. **Students who study neither Mathematics nor Science**:  
   These students are outside both sets \( M \) and \( S \).
   \[
   \text{Neither} = \text{Total students} - |M \cup S| = 50 - 45 = 5
   \]

---

### Summary of Answers:

1. **Only Mathematics**: 20 students
2. **Only Science**: 15 students
3. **Either Mathematics or Science**: 45 students
4. **Neither Mathematics nor Science**: 5 students

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Would you like additional explanation, or have any questions?

#### Related Questions:
1. How many students study only one subject?
2. What percentage of students study both Mathematics and Science?
3. If 5 more students join Mathematics, how does that affect the Venn Diagram?
4. How would this change if we added a third subject?
5. What is the probability a randomly selected student studies both subjects?

#### Tip:
For Venn Diagrams with two sets, use the formula \( |M \cup S| = |M| + |S| - |M \cap S| \) to find the union quickly.

Make a problem using Venn diagram with 2 circle and solution

Solve a Venn diagram problem involving students studying Mathematics and Science. This example includes calculating students who study only Mathematics, only Science, both subjects, or neither. Learn about set theory, Venn diagrams, and inclusion-exclusion principles in a step-by-step solution suitable for Grades 6-8.

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