In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach
mathematics and 4 teach physics and mathematics. How many teach physics?

We are given the following information:

- Total number of teachers: 20
- Number of teachers who teach mathematics: 12
- Number of teachers who teach both mathematics and physics: 4

Let:
- \( P \) be the number of teachers who teach physics.
- \( M \) be the number of teachers who teach mathematics (12).
- \( M \cap P \) be the number of teachers who teach both mathematics and physics (4).

We are tasked with finding the number of teachers who teach only physics, i.e., \( P \), without including those who teach both.

### Step 1: Calculate the number of teachers who teach only mathematics
The number of teachers who teach only mathematics is given by:
\[
M_{\text{only}} = M - (M \cap P) = 12 - 4 = 8
\]

### Step 2: Calculate the number of teachers who teach only physics
Let \( P_{\text{only}} \) be the number of teachers who teach only physics. The total number of teachers who teach either physics or mathematics is 20. Therefore:
\[
P_{\text{only}} + M_{\text{only}} + (M \cap P) = 20
\]
Substituting the known values:
\[
P_{\text{only}} + 8 + 4 = 20
\]
Simplifying this:
\[
P_{\text{only}} + 12 = 20
\]
\[
P_{\text{only}} = 20 - 12 = 8
\]

### Step 3: Calculate the total number of teachers who teach physics
The total number of teachers who teach physics, \( P \), includes those who teach only physics and those who teach both mathematics and physics:
\[
P = P_{\text{only}} + (M \cap P) = 8 + 4 = 12
\]

Thus, **12 teachers teach physics**.

Would you like further details on any step?

### Related Questions:
1. How many teachers teach only mathematics?
2. How many teachers teach both physics and mathematics?
3. If 5 teachers only teach physics, what would be the new total number of teachers?
4. If the total number of teachers increased to 25, how would that affect the calculations?
5. Can you visualize this problem using a Venn diagram?

**Tip**: In problems involving sets and overlapping categories, Venn diagrams can help visualize the relationships clearly.

In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach physics and mathematics. How many teach physics?

Learn how to calculate the number of teachers who teach physics in a school where some teach both mathematics and physics. This problem applies set theory and the inclusion-exclusion principle, using a step-by-step breakdown to solve it. Suitable for Grades 6-8 students.

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