If f(x) = x is my friend, and p(x) = x is perfect. then correct logical translation of the statement “some of my friends are not perfect” is _______.
∃ x (f(x) ∧ ¬ p(x))
“Some” requires an existential quantifier, and the same individual must be both a friend and not perfect. Thus the translation is \(\exists x\,(f(x)\land\neg p(x))\).
Important Questions from First Order Logic - Teaching
Consider the statements below:
“There is a country that borders both India and Nepal.”
Which of the following represents the above sentence correctly?A knowledge base contains only \(\exists x\,AsHighAs(x,Everest)\). Apply existential instantiation by introducing a fresh witness constant. Treat Kilimanjaro solely as a new symbol with no previously assigned geographical referent.
(a) \(AsHighAs(Everest,Everest)\)
(b) \(AsHighAs(Kilimanjaro,Everest)\)
Which applications are permitted by the fresh-constant rule?
Equivalent logical expression for the Well Formed Formula (WFF),
\(\sim(\forall x)\,F[x]\)
is
Let P(m, n) be the statement “m divides n” where the Universe of discourse for both the variables is the set of positive integers. Determine the truth values of the following propositions.
(a) \(\exists m \forall n P(m, n)\) (b) \(\forall n P(1, n)\) (c) \(\forall m \forall n P(m, n)\)
Codes :
________predicate calculus allows quantified variables to refer to objects in the domain of discourse and not to predicates or functions.
