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- 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
- 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
- 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
- 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
- is true provided P and Q are both true or both
- 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