1. **Problem Statement:** We are given three conditions for numbers: X is an even number, Y is a multiple of 3, and Z is less than 4. 2. **Understanding the conditions:** - X: Even numbers are integers divisible by 2, i.e., $X = 2k$ for some integer $k$. - Y: Multiples of 3 are integers divisible by 3, i.e., $Y = 3m$ for some integer $m$. - Z: Numbers less than 4 means $Z < 4$. 3. **Formulas and rules:** - Even numbers: $X = 2k$, where $k \in \mathbb{Z}$. - Multiples of 3: $Y = 3m$, where $m \in \mathbb{Z}$. - Inequality for Z: $Z < 4$. 4. **Example values:** - For X (even): 0, 2, 4, 6, ... - For Y (multiple of 3): 0, 3, 6, 9, ... - For Z (less than 4): any number less than 4, e.g., 3, 2, 1, 0, -1, ... 5. **Summary:** The problem defines sets of numbers based on divisibility and inequality conditions. These can be used in probability or counting problems involving balls or other objects. **Final answer:** - $X = \{2k \mid k \in \mathbb{Z}\}$ (even numbers) - $Y = \{3m \mid m \in \mathbb{Z}\}$ (multiples of 3) - $Z = \{z \in \mathbb{R} \mid z < 4\}$ (numbers less than 4)