Universal and existential quantifiers and basic predicate logic notation used beyond propositional logic.
30 cards · basic cards · AI-written, checked twice. Edit anything.
- What does the universal quantifier symbol ∀ represent?
Show answer
'for all' - asserts that a property holds for every element in the domain- What does the existential quantifier symbol ∃ represent?
Show answer
'there exists' - asserts that a property holds for at least one element in the domain- What is a predicate in predicate logic?
Show answer
A function that assigns true or false to objects; typically written P(x), Q(x,y), etc.- What does the notation P(x) mean?
Show answer
P is a predicate; x is a variable; truth value depends on what x represents- What is the domain or universe of discourse in predicate logic?
Show answer
The set of all objects that variables can refer to- What is the negation of the statement forall x, P(x)?
Show answer
∃x ¬P(x)- What is the negation of the statement there exists x, P(x)?
Show answer
∀x ¬P(x)- Translate to predicate logic: All humans are mortal.
Show answer
∀x (Human(x) → Mortal(x))- Translate to predicate logic: Some dogs are friendly.
Show answer
∃x (Dog(x) ∧ Friendly(x))- Translate to predicate logic: No integers are both odd and even.
Show answer
∀x (Integer(x) → ¬(Odd(x) ∧ Even(x)))- What is a free variable in a formula?
Show answer
A variable not bound by any quantifier; not in the scope of ∀ or ∃- What is a bound variable in a formula?
Show answer
A variable in the scope of a quantifier (∀ or ∃)- In the formula ∃x P(x, y), which variable is free and which is bound?
Show answer
x is bound; y is free- What is an open formula in predicate logic?
Show answer
A formula with at least one free variable; truth value depends on what the free variables represent- What is a closed formula or sentence in predicate logic?
Show answer
A formula with no free variables; every variable is bound by a quantifier
FlashKeepers