How Many Are Metric Spaces?

How many of the following pairs $(M, d)$ are metric spaces?

• $M = \mathbb{R}^n$ and $d\big((x_1, \ldots, x_n), (y_1, \ldots, y_n)\big) = \max_{1\le i \le n} |x_i - y_i|$

• $M = \{a, b, c, d\},$ where $d(a,b) = d(a,c) = 3$, $d(a,d) = d(b,c) = 7$, and $d(b,d) = d(c,d) = 11$

• $M = \mathcal{C}[0,1]$, the set of continuous functions $[0,1] \to \mathbb{R}$, and $d(f,g) = \max_{x\in [0,1]} |f(x) - g(x)|$

• $M = \mathcal{C}[0,1]$ and $d(f,g) = \int_{0}^{1} \big(f(x) - g(x)\big)^2 \, dx$