# Intermed. Logis Lesson 13-27

## 12 terms

### formal proof of validity

a step by step deduction of a conclusion from a set of premises, each step being justified by an appropriate basic rule

### rule of inference

a valid argument form which can be used to justify steps in a proof

### rules of replacement

forms of equivalent statements

### conditional proof

a special rule in a formal proof which allows us to assume the andecedent of a conditional and, once we deduce the consequent, to conclude the the entire conditional

a special rule which allows us to assume the negation of a proposition, deduce a self contradiction, then conclude the proposition

### truth-functionally complete

A set of logical operators is truth-functionally complete if and only if all possible combinations of true and false for two variables are derivable using only those logical operators

### NOR (∇)

equivalent to ~(p∨q), and truth-functionally complete

### decomposed

a compound proposition that is broken down into simple propositions (or the negation of simple propositions) which are called literals

### truth tree

a diagram which shows a set of propositions being decomposed into their literals

### recover the truth values

to determine, for a set of propositions, the truth values of the simple propositions for which the propositions in the set would all be true

### open branch

a path on a truth tree which includes no contradictions

### closed branch

a path on a truth tree for which a contradiction has been found