Sets And Relations

To solve the problem, we need to find the number of people who like both tea and coffee using the principle of inclusion-exclusion.

1. Understanding the Concepts:

- Total People: 50
- Number liking tea (T): 30
- Number liking coffee (C): 25
- Number liking neither: 10
- Use the formula for union: - People liking tea or coffee or both = total - neither

2. Given Values:

Total people = 50
Neither = 10 → People liking tea or coffee or both = 50 - 10 = 40
Tea (T) = 30
Coffee (C) = 25

3. Calculate Number Liking Both:

Final Answer:

The number of people who like both tea and coffee is 15.