To represent objects or individuals in a domain of discourse.

To describe properties or relations between objects.

To serve as a logical connective between propositions.

To quantify over a set of objects or values.

Terms are used to represent objects or individuals, while predicates are used to describe properties or relations.

Terms are used to quantify over a set of objects or values, while predicates are used to represent objects or individuals.

Terms are used to serve as logical connectives between propositions, while predicates are used to describe properties or relations.

Terms are used to represent properties or relations, while predicates are used to quantify over a set of objects or values.

To specify the number of objects or individuals that satisfy a given predicate.

To restrict the domain of discourse to a specific set of objects or individuals.

To introduce logical connectives between propositions.

To serve as predicates that describe properties or relations between objects.

A closed formula contains no free variables, while an open formula contains at least one free variable.

A closed formula contains only constants and predicates, while an open formula contains variables.

A closed formula is always true or false, while an open formula can be true or false depending on the values of its free variables.

A closed formula is a proposition, while an open formula is a predicate.

Any instance of a universally quantified formula is true.

Any instance of an existentially quantified formula is false.

Any closed formula is true.

Any open formula is false.

Any instance of a universally quantified formula is true.

Any instance of an existentially quantified formula is false.

Any closed formula is true.

Any open formula is false.

A model is a set of objects and relations that satisfies a given formula, while a structure is a set of objects and relations that satisfies a set of formulas.

A model is a set of objects and relations that satisfies a given formula, while a structure is a set of objects and relations that is consistent with a given formula.

A model is a set of objects and relations that satisfies a given formula, while a structure is a set of objects and relations that is equivalent to a given formula.

A model is a set of objects and relations that satisfies a given formula, while a structure is a set of objects and relations that is independent of a given formula.

Any formula that is true in all models is provable in predicate logic.

Any formula that is provable in predicate logic is true in all models.

Any formula that is true in some model is provable in predicate logic.

Any formula that is provable in predicate logic is true in some model.

Any formula that is true in all models is provable in predicate logic.

Any formula that is provable in predicate logic is true in all models.

Any formula that is true in some model is provable in predicate logic.

Any formula that is provable in predicate logic is true in some model.

A deductive argument is based on evidence, while an inductive argument is based on logic.

A deductive argument is based on logic, while an inductive argument is based on evidence.

A deductive argument is always valid, while an inductive argument is always invalid.

A deductive argument is always invalid, while an inductive argument is always valid.

A valid argument is based on logic, while a sound argument is based on evidence.

A valid argument is based on evidence, while a sound argument is based on logic.

A valid argument is always true, while a sound argument is always false.

A valid argument is always false, while a sound argument is always true.

A categorical syllogism has two premises and a conclusion, while a hypothetical syllogism has one premise and a conclusion.

A categorical syllogism has one premise and a conclusion, while a hypothetical syllogism has two premises and a conclusion.

A categorical syllogism has two premises and a conclusion, and the premises are categorical statements, while a hypothetical syllogism has one premise and a conclusion, and the premise is a hypothetical statement.

A categorical syllogism has one premise and a conclusion, and the premise is a categorical statement, while a hypothetical syllogism has two premises and a conclusion, and the premises are hypothetical statements.

A disjunctive syllogism has two premises and a conclusion, and the premises are disjunctive statements, while a conjunctive syllogism has one premise and a conclusion, and the premise is a conjunctive statement.

A disjunctive syllogism has one premise and a conclusion, and the premise is a disjunctive statement, while a conjunctive syllogism has two premises and a conclusion, and the premises are conjunctive statements.

A disjunctive syllogism has two premises and a conclusion, and the premises are categorical statements, while a conjunctive syllogism has one premise and a conclusion, and the premise is a hypothetical statement.

A disjunctive syllogism has one premise and a conclusion, and the premise is a categorical statement, while a conjunctive syllogism has two premises and a conclusion, and the premises are hypothetical statements.

A modal syllogism has two premises and a conclusion, and the premises are modal statements, while a non-modal syllogism has one premise and a conclusion, and the premise is a non-modal statement.

A modal syllogism has one premise and a conclusion, and the premise is a modal statement, while a non-modal syllogism has two premises and a conclusion, and the premises are non-modal statements.

A modal syllogism has two premises and a conclusion, and the premises are categorical statements, while a non-modal syllogism has one premise and a conclusion, and the premise is a hypothetical statement.

A modal syllogism has one premise and a conclusion, and the premise is a categorical statement, while a non-modal syllogism has two premises and a conclusion, and the premises are hypothetical statements.