https://file.aiquickdraw.com/mathbot/file/1729096121121593dm1ab.jpg

The problem presented in the image reads as follows:

**Problem Statement:**
"A survey carried out in a certain district showed that out of 215 teachers:
- 170 taught Math
- 130 taught Physics
- 44 taught Computer Studies
- 65 taught Math and Physics
- 26 taught Computer Studies and Physics
- 40 taught Computer Studies and Math"

**Question:**
Use a Venn diagram to represent this information.

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To solve this, we'll need to organize the information into three sets: Math (M), Physics (P), and Computer Studies (C). We'll represent these sets in a Venn diagram and solve for the various regions based on the overlapping sets.

Let's break down the information:
- \( |M| = 170 \): Teachers who teach Math.
- \( |P| = 130 \): Teachers who teach Physics.
- \( |C| = 44 \): Teachers who teach Computer Studies.
- \( |M \cap P| = 65 \): Teachers who teach both Math and Physics.
- \( |P \cap C| = 26 \): Teachers who teach both Physics and Computer Studies.
- \( |M \cap C| = 40 \): Teachers who teach both Math and Computer Studies.

Using this, we will solve for the number of teachers who fall into the different combinations of these subjects, and we will also check for any regions where all three subjects overlap.

### Steps to follow:
1. Assign variables to each region of the Venn diagram (representing teachers who teach combinations of the subjects).
2. Use the given information to create a system of equations to solve for the unknowns.
3. Construct the Venn diagram and calculate the numbers for each region.

Would you like me to solve this fully and draw the corresponding Venn diagram, or do you have any specific questions about this problem?

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**Related Questions:**
1. How do you calculate the number of teachers who teach all three subjects?
2. How can you verify that the total number of teachers sums up to 215?
3. What is the difference between the union and intersection of sets in Venn diagrams?
4. Can a Venn diagram be used to solve more complex scenarios with more than three sets?
5. How can Venn diagrams be applied in other fields besides education?

**Tip:** When working with Venn diagrams, it helps to start by filling in the overlaps (intersections) first, then subtract from the total to find the remaining regions.

A survey carried out in a certain district showed that out of 215 teachers: 170 taught Math, 130 taught Physics, 44 taught Computer Studies, 65 taught Math and Physics, 26 taught Computer Studies and Physics, 40 taught Computer Studies and Math. Represent the information in a Venn diagram.

Learn how to use a Venn diagram to represent a survey of 215 teachers and their subjects: Math, Physics, and Computer Studies. This problem involves set theory concepts, intersections, and unions, suitable for students in Grades 9-11.

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