Problem 1. Suppose that an agent has a preference, denoted by a binary relation R (and thus, a strict preference and an indifference relation are written by using P and I), for consumption bundles (x1, x2), where x,- is the consumption level of good i = 1, 2. The agent's preference is assumed to satisfy Strict Monotonicity, Order, Continuity, and Strict Convexity, so that it is represented by a utility function U (x1, x2). Choose below all correct explanations regarding this agent; write your answer choice(s). (2 marks) (a) U(x1,xz) = U(y1,yg) holds if x1 = 321 and x2 > yg. (b) If (x1,x2)P(yl,y2), then U(x1, x2) > U01,y2) holds. (c) If (x1,x2)1(yl,y2), then U(x1,x2) > Wynn) holds. (d) If U(x1,x2) = U(y1,y2), then U(z1,z2) > 004,\") where 2,, = %x,- + %y,- for each i = 1,2. (9) Indifference curves of this agent are upward-sloping. (f) If(X1,X2)P()'1,y2) and 071,372)1'(Z1,Z2), then U(X1,X2) > U(Z1,z2)