Discrete Math - Propositional and Predicate Logic

What is the difference between propositional logic and predicate logic?

• Propositional logic deals with propositions or statements that are either true or false, while predicate logic deals with predicates or properties that can be true or false for different objects or individuals.

• Propositional logic deals with mathematical equations, while predicate logic deals with natural language statements.

• Propositional logic deals with individual objects, while predicate logic deals with sets of objects.

• Propositional logic deals with deductive reasoning, while predicate logic deals with inductive reasoning.

State the Law of Excluded Middle in propositional logic.

• Both P and not P

• Either P or not P

• Neither P nor not P

• Either P and not P

What is a tautology in propositional logic?

• A tautology is a statement that is always true.

• A tautology is a statement that is never true.

• A tautology is a statement that is sometimes true and sometimes false.

• A tautology is a statement that is always false.

What is a contradiction in propositional logic?

• A contradiction in propositional logic is a statement or proposition that is always false.

• A contradiction in propositional logic is a statement or proposition that is sometimes true.

• A contradiction in propositional logic is a statement or proposition that is always true.

• A contradiction in propositional logic is a statement or proposition that is always uncertain.

What is a valid argument in predicate logic?

• An argument that is based on emotions rather than logic.

• An argument that is supported by personal anecdotes.

• The conclusion logically follows from the premises based on the rules of predicate logic.

• An argument that contains contradictory premises.

What is the Universal Quantifier in predicate logic?

• ∃

• ∈

• ⊢

• ∀

What is the Existential Quantifier in predicate logic?

• ∀

• ∈

• ∃

• ∧

State the Law of Universal Instantiation in predicate logic.

• If ∀x P(x) is true, then P(a) is true for any particular object a in the domain.

• If ∃x P(x) is true, then P(a) is true for all particular objects a in the domain.

• If ∃x P(x) is true, then P(a) is true for some particular object a in the domain.

• If ∃x P(x) is true, then P(a) is true for any particular object a in the domain.

State the Law of Universal Generalization in predicate logic.

• If P(x) is true for all x in the domain, then ∀x P(x) is true.

• If P(x) is true for at least one x in the domain, then ∀x P(x) is true.

• If P(x) is true for none of the x in the domain, then ∀x P(x) is true.

• If P(x) is true for some x in the domain, then ∀x P(x) is true.

What is the difference between a valid argument and a sound argument in predicate logic?

• A valid argument is one where the conclusion logically follows from the premises, while a sound argument is a valid argument with all true premises.

• A valid argument is one where the conclusion logically follows from the premises, while a sound argument is a valid argument with at least one false premise.

• A valid argument is one where the conclusion does not logically follow from the premises, while a sound argument is a valid argument with all true premises.

• A valid argument is one where the conclusion logically follows from the premises, while a sound argument is a valid argument with all false premises.