Solve the compound inequality. Graph the solution set and write it in interval notation \[ x \leq 2 \text { and } x \geq 3 \]

Step 1 ：Solve the compound inequality: \(x \leq 2\) and \(x \geq 3\).

Step 2 ：Notice that there is no number that is both less than or equal to 2 and greater than or equal to 3.

Step 3 ：Therefore, the solution set is empty, which in interval notation is denoted as \(\emptyset\).

Step 4 ：\(\boxed{\emptyset}\) is the final answer.