Topic 1: Predicate Logic

Which of the following symbols represents the universal quantifier in predicate logic?

• ∃

• ∀

• →

• ∧

Which of the following best describes the relationship between propositional logic and predicate logic?

• Predicate logic is a generalization of propositional logic.

• Propositional logic is a generalization of predicate logic.

• Predicate logic and propositional logic are equivalent in expressiveness.

• Predicate logic and propositional logic are unrelated.

Which of the following is a valid rule of inference in predicate logic?

• Modus ponens

• Modus operandi

• Law of contradiction

• Principle of modus

What does the existential quantifier in predicate logic express?

• A statement is true for all elements in the domain.

• There exists at least one element in the domain for which a statement is true.

• A statement is true for some, but not all, elements in the domain.

• A statement is true for exactly one element in the domain.

Consider the following predicate logic statement: ∀x (P(x) → Q(x)). If we know that ∀x P(x), what can we conclude?

• ∀x Q(x)

• ∃x Q(x)

• ∀x (P(x) ∧ Q(x))

• ∃x (P(x) ∧ Q(x))

Given the predicates P(x): x is an even number and Q(x): x is a multiple of 4, which of the following predicate logic statements correctly expresses "All even numbers are multiples of 4"?

• ∀x (P(x) → Q(x))

• ∀x (Q(x) → P(x))

• ∃x (P(x) ∧ Q(x))

• ∃x (P(x) → Q(x))

Consider the following predicates: P(x): x is a student, Q(x): x is smart, R(x): x is diligent. Which of the following statements is the correct representation of "All smart students are diligent"?

• ∀x (P(x) ∧ Q(x) → R(x))

• ∀x (P(x) → Q(x) ∧ R(x))

• ∀x ((P(x) → Q(x)) → R(x))

• ∀x (P(x) ∧ (Q(x) → R(x)))