Chapter 7 - Elementary Metamathematics

Question 1

The conclusion of an argument is a ______ _______ of its premises if and only if any truth-value assignment that makes all the premises true also makes the conclusion true.

Answer 1

logical consequence

Question 2

Two formulae are ______ _______ if and only if they receive the same truth-value on every truth-value assignment.

Answer 2

logically equivalent

Question 3

A ______ is either a sentential letter (e.g.,

P, Q, T, etc.) or a negated sentential letter (e.g., ¬P, ¬Q, ¬S, etc.).

Answer 3

literal

Question 4

A formula of sentential logic is in ______ ______ ______ if and only if it is one of the following:
A literal;
A conjunction of literals;
A disjunction of conjunctions of literals.

Answer 4

disjunctive normal form

Question 5

A formula of sentential logic is in ______ ______ ______ if and only if it is one of the following:
A literal;
A disjunction of literals;
A conjunction of disjunctions of literals.

Answer 5

conjunctive normal form