Which of the following is/are metric on \(\mathbb{R}\)-
(a) \( d(x,y)=|sin(x-y)|\)
(b) \(d(x,y)=|x|\)
(c) \(d(x,y)=min\{1, d'(x,y)\}\) where \(d'\) is a metric
(d) \(d(x,y)=max\{1, d'(x,y)\}\) where \(d'\) is a metric
Explanation: (c) is the correct answer.
(a) is not correct as \(\pi \ne 0\) but \(\sin(\pi-0)=0\).
(b) is not a metric as \(0 \ne 1\) but \(d(0,1)=0\).
(d) is not a metric as \(d(1,1)\ne 0\)
Tags:
Metric