From Wolf:

- A
*proposition*is any declarative statement (including mathematical sentences such as equations) that is true or false. - We use the letters as
*propositional variables*. That is, we let these letters stand for or represent statements. - Five symbols, called
*connectives*, are used to stand for the following words:- for ``and''.
*Conjunction*. - for ``or''.
*Disjunction*. - for ``not''.
*Negation*. - for ``implies'' or ``if...then''.
*Conditional*or*Implication*. - for ``if and only if''.
*Biconditional*or*Equivalence*.

- for ``and''.
- A statement that is not built up from simpler ones by
connectives and/or quantifiers is called
*atomic*or*simple*. (Quantifiers will be introduced later.) A statement that is built up from simpler ones is called*compound*. - The
*truth functions*of the connectives are defined as follows:- is true provided
*P*and*Q*are both true. - is true provided at least one of the statements
*P*and*Q*is true. - is true provided
*P*is false. - is true provided
*P*is false, or*Q*is true (or both). - is true provided
*P*and*Q*are both true or both false.

- is true provided
- A
*tautology*, or a*law of propositional logic*, is a statement whose truth function has all*T*'s as outputs. - A
*contradition*is a statement whose truth function has all*F*'s as outputs (in other words, it's a statement whose negation is a tautology). - Two statements and are called
*propositionally equivalent*if is a tautology.

Wed Nov 18 12:16:44 EST 1998