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GATE | GATE-CS-2003 | Question 31
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
Please comment below if you find anything wrong in the above post
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