## Discussion Forum

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 |