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Que. Let (5, ≤) be a partial order with two minimal elements a and b, and a maximum element c.

Let P : S → {True, False} be a predicate defined on S.
Suppose that P(a) = True, P(b) = False and
P(x) ⇒ P(y) for all x, y ∈ S satisfying x ≤ y,
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 x ≠ a and x ≠ c
c. P(x) = False for all x ∈ S such that b ≤ x 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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