**Question:**

Give $ A = [1, 4]; B = (2, 6); C = (1, 2) $. Find $ A \cap B \cap C $.

**Answer**

Recall: $ x \in A \cap B \cap C \Leftrightarrow \begin {cases} x \in A \\x \in B \\x \in C \end {cases} $

We need to find the numbers $ x $ such that $ \begin {cases} x \in [1; 4] \\x \in (2; 6) \\x \in (1; 2) \end {cases} $

It’s easy to see that there is no $ x $ number that satisfies this.

In a nutshell $ A \cap B \cap C = \emptyset $.