19.1.1.3 Properties of metric spaces

Condition: Are the following functions a metric on the real line: a) \( \rho(x, y)=\sin ^{2}(x-y) \) b) \( \rho(x, y)=\sqrt{|x-y|} \) c) \( \rho(x, y)=\left|e^{x}-e^{y}\right| \).