This problem considers two new choice axioms, which well call A and B

A: If x,y C(A) and x,y B, then either x,y C(B) or x,y / C(B).

B: If xC(A) and AB, then either xC(B) or C(B)A=.

also consider the following properties

Sen's beta: Suppose that x, y A B, x C(A) and y C(A). Then x C(B) if and only if y C(B).

Sen's alpha: Suppose that x A B and x C(B). Then x C(A).

WARP: Suppose that x, y A, x, y B, x C (A), and y / C (A). Then y / C (B).

1. Prove that A is stronger than Sens in the following sense:

a If A holds, then Sens holds. b Sens can hold even when A does not.

2. Is Sens and Sens combined yield the same result as the combination of A&B? If so, prove it. If not, provide a counterexample.