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First-Order Predicate Logic

This quiz covers the fundamentals of First-Order Predicate Logic, including syntax, semantics, and inference rules.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Which of the following is a valid syntax for a first-order predicate logic statement?

  1. ∀x(Px → Qx)
  2. ∃x(Px ∧ Qx)
  3. (Px ∨ Qx) → ∀x(Px ∨ Qx)
  4. None of the above
Question 2 Multiple Choice (Single Answer)

What is the meaning of the predicate symbol 'P(x)' in first-order predicate logic?

  1. It represents a property that can be true or false for an object x.
  2. It represents a set of objects that satisfy a certain condition.
  3. It represents a function that maps an object x to a truth value.
  4. None of the above
Question 3 Multiple Choice (Single Answer)

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

  1. Modus ponens
  2. Modus tollens
  3. Hypothetical syllogism
  4. All of the above
Question 4 Multiple Choice (Single Answer)

What is the difference between a universal quantifier (∀) and an existential quantifier (∃) in first-order predicate logic?

  1. A universal quantifier asserts that a property holds for all objects in a domain, while an existential quantifier asserts that it holds for at least one object.
  2. A universal quantifier asserts that a property holds for some objects in a domain, while an existential quantifier asserts that it holds for all objects.
  3. A universal quantifier asserts that a property holds for no objects in a domain, while an existential quantifier asserts that it holds for some objects.
  4. None of the above
Question 5 Multiple Choice (Single Answer)

What is the negation of the statement "∀x(Px → Qx)" in first-order predicate logic?

  1. ∃x(Px ∧ ¬Qx)
  2. ∃x(¬Px ∨ Qx)
  3. ∀x(¬Px ∨ Qx)
  4. None of the above
Question 6 Multiple Choice (Single Answer)

Which of the following is a valid first-order predicate logic statement?

  1. ∀x(Px → Qx) ∧ ∃x(¬Px)
  2. ∀x(Px → Qx) → ∃x(¬Qx)
  3. ∃x(Px ∧ Qx) → ∀x(Px ∨ Qx)
  4. None of the above
Question 7 Multiple Choice (Single Answer)

What is the domain of discourse in first-order predicate logic?

  1. The set of all objects under consideration.
  2. The set of all properties under consideration.
  3. The set of all statements under consideration.
  4. None of the above
Question 8 Multiple Choice (Single Answer)

Which of the following is a valid first-order predicate logic statement?

  1. ∀x(Px ∨ Qx) → (∀xPx ∨ ∀xQx)
  2. ∃x(Px ∧ Qx) → (∃xPx ∧ ∃xQx)
  3. ∀x(Px → Qx) → (∃xPx → ∃xQx)
  4. None of the above
Question 9 Multiple Choice (Single Answer)

What is the difference between a constant symbol and a variable symbol in first-order predicate logic?

  1. A constant symbol represents a specific object, while a variable symbol represents any object in the domain of discourse.
  2. A constant symbol represents any object in the domain of discourse, while a variable symbol represents a specific object.
  3. A constant symbol represents a property, while a variable symbol represents an object.
  4. None of the above
Question 10 Multiple Choice (Single Answer)

Which of the following is a valid first-order predicate logic statement?

  1. ∀x(Px → Qx) → (∃xPx → ∃xQx)
  2. ∃x(Px ∧ Qx) → (∃xPx ∨ ∃xQx)
  3. ∀x(Px ∨ Qx) → (∃xPx ∧ ∃xQx)
  4. None of the above
Question 11 Multiple Choice (Single Answer)

What is the difference between a term and a formula in first-order predicate logic?

  1. A term is a constant symbol, a variable symbol, or a function symbol applied to terms, while a formula is a statement that can be true or false.
  2. A term is a statement that can be true or false, while a formula is a constant symbol, a variable symbol, or a function symbol applied to terms.
  3. A term is a constant symbol or a variable symbol, while a formula is a function symbol applied to terms.
  4. None of the above
Question 12 Multiple Choice (Single Answer)

Which of the following is a valid first-order predicate logic statement?

  1. ∀x(Px → Qx) → (∀xPx → ∀xQx)
  2. ∃x(Px ∧ Qx) → (∃xPx ∧ ∃xQx)
  3. ∀x(Px ∨ Qx) → (∀xPx ∨ ∃xQx)
  4. None of the above
Question 13 Multiple Choice (Single Answer)

What is the difference between a closed formula and an open formula in first-order predicate logic?

  1. A closed formula contains no free variables, while an open formula contains at least one free variable.
  2. A closed formula contains at least one free variable, while an open formula contains no free variables.
  3. A closed formula is a statement that can be true or false, while an open formula is a term.
  4. None of the above
Question 14 Multiple Choice (Single Answer)

Which of the following is a valid first-order predicate logic statement?

  1. ∀x(Px ∨ Qx) → (∀xPx ∨ ∃xQx)
  2. ∃x(Px ∧ Qx) → (∃xPx ∨ ∀xQx)
  3. ∀x(Px → Qx) → (∃xPx ∨ ∀xQx)
  4. None of the above
Question 15 Multiple Choice (Single Answer)

What is the difference between a model and a structure in first-order predicate logic?

  1. A model is a set of objects and a set of relations on those objects, while a structure is a set of objects, a set of relations on those objects, and a set of functions on those objects.
  2. A model is a set of objects, a set of relations on those objects, and a set of functions on those objects, while a structure is a set of objects and a set of relations on those objects.
  3. A model is a set of objects and a set of functions on those objects, while a structure is a set of objects, a set of relations on those objects, and a set of functions on those objects.
  4. None of the above
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