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?

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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?

1.P(x) = True for all x S such that x ≠ b

2.P(x) = False for all x ∈ S such that b ≤ x and x ≠ c

3.P(x) = False for all x ∈ S such that x ≠ a and x ≠ c

4.P(x) = False for all x ∈ S such that a ≤ x and b ≤ x

Posted Date:-2022-05-13 09:08:31

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