GATE | CS | 2003 | Discrete Mathematics | Set Theory | Question 31

Last Updated :
Discuss
Comments

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 ?

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

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

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

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

This question is part of this quiz :

Set Theory & Algebra,GATE-CS-2003,Partial Order and Lattices for GATE,Discrete mathematics PYQ GATE QUIZ
Tags:
Engineering Mathematics Questions
GATE
GATE CS
Discrete Mathematics
Share your thoughts in the comments