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(Solved): For xR1 and yR1, define d1(x,y)=(xy)2,d2(x,y)=xy,d3(x,y)=x2y2 ...


For \( x \in R^{1} \) and \( y \in R^{1} \), define \[ \begin{array}{l} d_{1}(x, y)=(x-y)^{2}, \\ d_{2}(x, y)=\sqrt{|x-y|}, \

For and , define Determine, for each of these, whether it is a metric or not.


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Let X be a non-empty set and dbe a map defined d:X?R a metric on Xif the following properties holds:(1) d(x,y)>0,?x?y.(2)d(x,y)=0?x=y,?x?X(3)d(x,y)=d
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