In a pollution study of 1500 Indian rivers the following data were reported. 520 were polluted by sulphur compounds, 335 were polluted by phosphates, 425 were polluted by crude oil, 100 were polluted by both crude oil and sulphur compounds, 180 were polluted by both sulphur compounds and phosphates, 150 were polluted by both phosphates and crude oil and 28 were polluted by sulphur compounds, phosphates and crude oil. How many of the rivers were polluted by atleast one of the three impurities?
How many of the rivers were polluted by exactly one of the three impurities?

Explanation

To solve the problem, we will use the principle of inclusion-exclusion to find the number of rivers polluted by at least one impurity and then calculate how many were polluted by exactly one impurity.

### Step 1: Define the Sets
Let:
- \( S \) = Set of rivers polluted by sulphur compounds
- \( P \) = Set of rivers polluted by phosphates
- \( C \) = Set of rivers polluted by crude oil

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