Que: 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
Answer: P(x) = False for all x ∈ S such that a ≤ x and b ≤ x

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