### Theory:

Important!
We have already the learned the cardinality of sets and practical problems for two sets. Now, let us going to solve practical problems for three sets.
For any three finite sets $$A$$, $$B$$ and $$C$$:

$$n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(B \cap C) - n(A \cap C) + n(A \cap B \cap C)$$
Solving practical problems using Venn diagram
Let us say, three sets $$A$$, $$B$$ and $$C$$ represents the employees in a company.

From the above Venn diagram, we can conclude the following:

1. Number of employees in set $$A = a + x + z + r$$

2. Number of employees in set $$B = b + x + y + r$$

3. Number of employees in set $$C = c + y + z + r$$

4. Number of employees in exactly (common) three sets $$= r$$

5. Number of employees in set $$A$$ only $$= a$$

6. Number of employees in set $$B$$ only $$= b$$

7. Number of employees in set $$C$$ only $$= c$$

8. Total number of employees in only one set $$= (a + b + c)$$

9. Total number of employees in only two sets $$= (x + y + z)$$

10. Total number of employees in at least two sets (two or more sets) $$= (x + y + z + r)$$

11. Total number of employees in all the three sets $$= (a + b + c + x + y + z + r)$$