Bob's preferences are rational, convex, continuous, and locally non-satiated. Suppose that he is indifferent between the consumption bundles he chooses at (p, w) and (p, w); that is, x(p, w) x(p, w). Let p = 1/2 (p + p) and w'' =1/2(w+w'), and suppose that p' doesn't equal to p and w doesn't equal to w'.

(a) Is it true, false, or uncertain that x(p, w) x(p, w)? Why?

(b) Is it true, false, or uncertain that x(p, w) x(p, w)? Why?