Let's break down the Venn diagram shown in the image and answer the questions one by one.

1. How many students are taking math?

In the Venn diagram, the entire Math circle represents students taking Math. This includes the following regions:

• 6 (only Math)
• 14 (Math and History)
• 8 (Math and Science)
• 2 (Math, Science, and History)

So, the total number of students taking Math is: $6 + 14 + 8 + 2 = 30$ Thus, 30 students are taking Math.

2. How many students are taking science and history?

Students taking both Science and History are represented by the overlap between the Science and History circles, which includes:

• 2 (Math, Science, and History)
• 5 (Science and History only)

So, the total number of students taking Science and History is: $2 + 5 = 7$ Thus, 7 students are taking both Science and History.

3. How many students are taking math and science, but not history?

Students taking Math and Science but not History are represented by the section where Math and Science overlap but exclude History. This is the region with:

• 8 (Math and Science only)

Thus, 8 students are taking Math and Science, but not History.

Would you like further details on any of these? Here are five related questions to explore:

1. How many students are taking only Science?
2. How many students are taking at least two subjects?
3. How many students are taking exactly one subject?
4. How many students are taking all three subjects (Math, Science, and History)?
5. How many students are taking History but not Math?

Tip: When working with Venn diagrams, it's helpful to carefully analyze each overlapping region to avoid counting the same group twice.