2. A metric function is defined as a real valued function having the following three properties. (a) d(x,y)= 0 iffx=y (b) d(x,y)=d(y,z) (c) d(x, y) + d(y,z) 2 d(x, z). Show that Hamming distance and Asymmetric distance, which are defined below, are metric functions. Let (X, Y) be the number of 1 0 crossovers from X to Y. Then, the Ham- ming distance, DH(X,Y) -N(X, Y) + N(Y, X) and the asymmetric distance, DA(X,Y) max{N(X, Y), N(Y, X)) 2. A metric function is defined as a real valued function having the following three properties. (a) d(x,y)= 0 iffx=y (b) d(x,y)=d(y,z) (c) d(x, y) + d(y,z) 2 d(x, z). Show that Hamming distance and Asymmetric distance, which are defined below, are metric functions. Let (X, Y) be the number of 1 0 crossovers from X to Y. Then, the Ham- ming distance, DH(X,Y) -N(X, Y) + N(Y, X) and the asymmetric distance, DA(X,Y) max{N(X, Y), N(Y, X))