Q31

MCQ2 marks, −0.5

Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S $\to$ {True, False} be a predicate defined on S. Suppose that P(a) = True, P(b) = False and P(x) $\implies$ P(y) for all $x, y \in S$ satisfying $x \leq y$ , where $\implies$ stands for logical implication. Which of the following statements CANNOT be true?

(A)

P(x) = True for all x $\in$ S such that x ≠ b

(B)

P(x) = False for all x $\in$ S such that x ≠ a and x ≠ c

(C)

P(x) = False for all x $\in$ S such that b ≤ x and x ≠ c

(D)

P(x) = False for all x $\in$ S such that a ≤ x and b ≤ x

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