Definitions

From Wolf:

1. A proposition is any declarative statement (including mathematical sentences such as equations) that is true or false.
2. We use the letters as propositional variables. That is, we let these letters stand for or represent statements.
3. Five symbols, called connectives, are used to stand for the following words:
   1. for ``and''. Conjunction.
   2. for ``or''. Disjunction.
   3. for ``not''. Negation.
   4. for ``implies'' or ``if...then''. Conditional or Implication.
   5. for ``if and only if''. Biconditional or Equivalence.
4. 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.
5. The truth functions of the connectives are defined as follows:
   1. is true provided P and Q are both true.
   2. is true provided at least one of the statements P and Q is true.
   3. is true provided P is false.
   4. is true provided P is false, or Q is true (or both).
   5. is true provided P and Q are both true or both false.
6. A tautology, or a law of propositional logic, is a statement whose truth function has all T's as outputs.
7. 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).
8. Two statements and are called propositionally equivalent if is a tautology.