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Syntax of Predicate Logic

Description: This quiz covers the syntax of predicate logic, including the formation of terms, formulas, and sentences.
Number of Questions: 15
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Tags: predicate logic syntax
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Which of the following is a term in predicate logic?

  1. All men are mortal

  2. Socrates is a man

  3. The number of planets in our solar system is eight

  4. Every dog has its day

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Correct Option: B
Explanation:

A term in predicate logic is a constant, a variable, or a function term.

Which of the following is a formula in predicate logic?

  1. All men are mortal

  2. Socrates is a man

  3. The number of planets in our solar system is eight

  4. Every dog has its day

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Correct Option: A
Explanation:

A formula in predicate logic is a well-formed expression that can be either true or false.

Which of the following is a sentence in predicate logic?

  1. All men are mortal

  2. Socrates is a man

  3. The number of planets in our solar system is eight

  4. Every dog has its day

Show answer
Correct Option: D
Explanation:

A sentence in predicate logic is a formula that does not contain any free variables.

Which of the following is a constant in predicate logic?

  1. x

  2. y

  3. Socrates

  4. The number 7

Show answer
Correct Option: C
Explanation:

A constant in predicate logic is a symbol that refers to a specific object.

Which of the following is a variable in predicate logic?

  1. x

  2. y

  3. Socrates

  4. The number 7

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Correct Option: A
Explanation:

A variable in predicate logic is a symbol that can refer to any object in the domain of discourse.

Which of the following is a function term in predicate logic?

  1. father(John)

  2. brother(Mary)

  3. sister(Bob)

  4. All men are mortal

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Correct Option: A
Explanation:

A function term in predicate logic is a term that is formed by applying a function symbol to one or more arguments.

Which of the following is a predicate in predicate logic?

  1. All men are mortal

  2. Socrates is a man

  3. The number of planets in our solar system is eight

  4. Every dog has its day

Show answer
Correct Option: B
Explanation:

A predicate in predicate logic is a property or relation that can be applied to one or more objects.

Which of the following is a quantifier in predicate logic?

  1. All

  2. Some

  3. No

  4. Every

Show answer
Correct Option: A
Explanation:

A quantifier in predicate logic is a symbol that indicates the scope of a variable.

Which of the following is a logical connective in predicate logic?

  1. And

  2. Or

  3. Not

  4. If...then

Show answer
Correct Option: A
Explanation:

A logical connective in predicate logic is a symbol that connects two or more formulas.

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

  1. Modus ponens

  2. Modus tollens

  3. Hypothetical syllogism

  4. Disjunctive syllogism

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Correct Option: A
Explanation:

A rule of inference in predicate logic is a rule that allows us to derive new formulas from given formulas.

Which of the following is a proof in predicate logic?

  1. A sequence of formulas that starts with axioms and ends with a theorem

  2. A sequence of formulas that is valid

  3. A sequence of formulas that is sound

  4. A sequence of formulas that is complete

Show answer
Correct Option: A
Explanation:

A proof in predicate logic is a sequence of formulas that starts with axioms and ends with a theorem.

Which of the following is a model in predicate logic?

  1. A set of objects and a set of relations on those objects

  2. A set of formulas that is consistent

  3. A set of formulas that is complete

  4. A set of formulas that is valid

Show answer
Correct Option: A
Explanation:

A model in predicate logic is a set of objects and a set of relations on those objects.

Which of the following is a theorem in predicate logic?

  1. A formula that is true in every model

  2. A formula that is valid

  3. A formula that is sound

  4. A formula that is complete

Show answer
Correct Option: A
Explanation:

A theorem in predicate logic is a formula that is true in every model.

Which of the following is a valid argument in predicate logic?

  1. An argument that has a true conclusion and true premises

  2. An argument that has a false conclusion and false premises

  3. An argument that has a true conclusion and false premises

  4. An argument that has a false conclusion and true premises

Show answer
Correct Option: A
Explanation:

A valid argument in predicate logic is an argument that has a true conclusion and true premises.

Which of the following is a sound argument in predicate logic?

  1. An argument that has a true conclusion and true premises

  2. An argument that has a false conclusion and false premises

  3. An argument that has a true conclusion and false premises

  4. An argument that has a false conclusion and true premises

Show answer
Correct Option: A
Explanation:

A sound argument in predicate logic is an argument that has a true conclusion and true premises.

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