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Let X be a non-empty set. [Each part is worth 5pt] \text { (a) Let } d: X \times X \rightarrow \mathbf{R}_{+} \text {be defined as } d(x, y)=\left\{\begin{array}{ll} 0

& \text { if } x=y \\ 1 & \text { if } x \neq y \end{array}\right. Show that d is a metric on X. This metric is called discrete. (b) Let d be a metric on X and let f : R4 → R4. If ƒ is strictly increasing, is it true that fod is a metric on X?

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