a) Let (X,d) be a metric space. Given a point x € X and a real number r > 0. show that A = {y e X:d(x,y) >r} is open in X. b) Let (X, d) be a metric space. Prove that |d(x,y) - d(z,w) |≤ (x,z) + d(y,w), Ɐ x,y,z,w ϵX.