Please solve both the questions with proper explanations and clear steps. Give the reason or example if they are not a distance metric. Give proper explanation why they are not distance metric. Verify for all the 3 or 4 properties of a distance metric

Let c:R2nR0 be defined as c(x,y)={10ifx=yo.w. Define a distance d:XXR0 as d(x,y)=inic(xi,yi),i1in. Is d() a metric? Suppose d0,d1 are metrics. Are the following also metrics? Justify your answer. i. d0d1 ii. (d0+d1)/(d0d1) iii. max{d0,d1} iv. Let X be a finite set. Define a distance d:XXR0 as d(x,y)=xy+1xy