If in a group of people, $40$ like tea, $30$ like coffee, and $20$ like both tea and coffee, how many people like only tea?

Let the set of people who like tea be $T$ and coffee be $C$.
From the given information:

* Total people who like tea, $n(T)=40$
* People who like both tea and coffee, $n(T\cap C)=20$

To find the number of people who like only tea, we subtract the overlapping section from the total tea-preferring group:

$$\text{People who like only tea}=n(T)-n(T\cap C)$$

$$\text{People who like only tea}=40-20=20$$