Let (A, ) be a partial order with two minimal elements a, b and a maximum element c. Let P:A > {True, False} be a predicate defined on A. Suppose that P(a) = True, P(b) = False and P(a) P(b) for all satisfying a b, where stands for logical implication. Which of the following statements cannot be true?

• A. P(x) = True for all x S such that x b
• B. P(x) = False for all x S such that b x and x c
• C. P(x) = False for all x S such that x a and x c
• D. P(x) = False for all x S such that a x and b x