If 60 people in a city like cricket, 30 like football and 20 like both cricket and football, how many people like only cricket?

Let C be the set of people who like cricket, and F be the set of people who like football.

Given:
|C| = 60 (number of people who like cricket)
|F| = 30 (number of people who like football)
|C ∩ F| = 20 (number of people who like both cricket and football)

We want to find the number of people who like only cricket. This can be represented as |C - (C ∩ F)|, which is the number of people in C but not in the intersection of C and F.

Using the principle of inclusion-exclusion, we have:
|C ∪ F| = |C| + |F| - |C ∩ F|
|C ∪ F| = 60 + 30 - 20 = 70

The number of people who like only cricket is:
|C| - |C ∩ F| = 60 - 20 = 40

Therefore, 40 people like only cricket.