Propositional-Logic

Question 20

Consider the following first order logic formula in which R is a binary relation symbol.

 ∀x∀y (R(x, y)  => R(y, x))

The formula is

A	satisfiable and valid
B	satisfiable and so is its negation
C	unsatisfiable but its negation is valid
D	satisfiable but its negation is unsatisfiable

Engineering-MathematicsPropositional-LogicGATE 2006-IT

Question 20 Explanation:

The given relation is known to be symmetry. We have both symmetric relations possible as well as antisymmetric but neither always holds for all sets. So they both are valid but are satisfiable.

Correct Answer: B

Question 20 Explanation:

The given relation is known to be symmetry. We have both symmetric relations possible as well as antisymmetric but neither always holds for all sets. So they both are valid but are satisfiable.