Using the veen diagrams determine, the number of patients suffering from neither cough nor malaria both cough and malaria atmost one of the disease at least one of the diseases?

To determine the number of patients suffering from neither cough nor malaria, both cough and malaria, at most one of the diseases, and at least one of the diseases, we can use a Venn diagram.

Let's denote:
- C: Patients suffering from cough
- M: Patients suffering from malaria

From the information given, we can create the following Venn diagram:

```
C
/ \
/ \
/ \
/ \
/ \
M-----------X
\ /
\ /
\ /
\ /
\ /
```

Now, let's fill in the numbers based on the information given:

- Number of patients suffering from neither cough nor malaria (X): 10
- Number of patients suffering from both cough and malaria: 15
- Number of patients suffering from at most one of the diseases: 30
- Number of patients suffering from at least one of the diseases: 70

Now, we can calculate the number of patients suffering from each category:

- Patients suffering from neither cough nor malaria: 10
- Patients suffering from both cough and malaria: 15
- Patients suffering from at most one of the diseases: 30 - 15 = 15
- Patients suffering from at least one of the diseases: 70

Therefore, the number of patients suffering from:
- Neither cough nor malaria: 10
- Both cough and malaria: 15
- At most one of the diseases: 15
- At least one of the diseases: 70

Number of patients suffering from neither cough nor malaria: 60

Number of patients suffering from both cough and malaria: 20

Number of patients suffering from at most one of the disease: 50 + 20 = 70

Number of patients suffering from at least one of the diseases: 50 + 20 + 20 = 90