3. (12%) Consider the following relations on the set of integers, and answer the questions. Which of these relations are reflexive? Which of these relations are symmetric? Which of these relations are anti-symmetric? Which of these relations are transitive? Prove your answers.

$$\begin{array}{l} R _ {1} = \{(x, y) \mid (x - y) ^ {2} < 1 0 \} \\ R _ {2} = \{(x, y) \mid (x - y) \bmod 5 = 0 \} \\ R _ {3} = \{(x, y) \mid x \geq y + 3 \} \\ \end{array}$$