Let (X, d) be a complete metric space and A ⊆ X be a closed subset. Which of the following statements is always TRUE?

Which of the following statements is true for any metric space X?

Which of the following defines a metric on ℝ?

Let (X, d) be a metric space. Which of the following statements are true? 1. Every compact subset of (X, d) is closed and bounded. 2. Every closed and bounded subset of (X, d) is compact. 3. Every compact subset of (X, d) is open. 4. Any finite subset of (X, d) is compact.