August 26, 2004

Class exercises reviewed

Practice 5

Practice 6

Exercises: 7-10 any parts (p. 15)

15 (p. 16)

Other materials

Transparencies with important tables: tautologies, inferences, equivalences

An expression that is a legitimate string (syntactically) is called a well formed formula (WFF)

Order of precedence rules( p. 6) –

In a wff with a number of connectives, the connective to be applied last is the main connective - tree structure shown

A wff whose truth values are always true is called a tautology

A wff whose truth values are always false is called a contradiction

contradictions are represented by 0

tautologies are represented by 1

DeMorgan’s Laws are critical

Algorithm – definition and examples at end of section 1.1

proof by truth table

proof by contradiction

Definition on page 22: Proof sequence is a sequence of wffs in which each wff is either a hypothesis or the result of applying oneof the formal system’s derivation rules to earlier wffs in the sequence.

Derivation hints on page 26

• Use Modus ponens when possible
• Use Demorgan’s Laws – to remove parentheses with negations
• Convert P v Q to P’-> Q

Deduction rule – p 26

Hypothetical syllogism p. 27

Disjunctive syllogism