Which of these distance functions is a metric? If it is not a metric, state which of the four metric properties it violates. (a) Let X=R and define d(x,y)=xy. (b) Let be a finite set and X=m. The Hamming distance on X is d(x,y)= \# of positions on which x and y differ. (c) Squared Euclidean distance on Rm, that is, d(x,y)=i=1m(xiyi)2. (It might be easiest to consider the case m=1.)