Suppose X and X are both metric spaces, with metrics d_x, d_yrespectively.

a) Show that XxY can be made into a metric space using the metric for all (x,y),(x₂,y₂) in XxY, d((x,y),(x₂,y₂))=d_x(x₁,x₂) + d_y(y₁,y₂)

b) Show that x + y can be made into a metric space via metric defined: d((x,y),(x₂,y₂))= (dx(x,x₂)d_y(y,y₂))