Propositional
calculus is the branch of mathematics that deals with the rules of
logic and evaluation of statements or propositions. It is sometimes
referred to as sentential calculus for its use of the sentential
conjunctions. It is primarily concerned generating laws for
evaluating conjugated statements. Propositional calculus is part of a
broader science of logic and proof.
Some of the symbols
used in propositional calculus:
Symbol
|
Meaning
|
¬
|
Not or negation
|
^
|
and
|
v
|
or
|
→
|
implies
|
↔
|
If and only if
|
P
|
Sentential Statement
|
Q
|
Sentential
Statement
|
T
|
True
|
F
|
False
|
In propositional
calculus the above symbols are used in constructing truth tables for
evaluating compound or conjugated sentences. The truth tables
provide a short hand tool for deriving new laws from the simple
compound sentential statements. Truth tables like the one below
shows some of the simple rules and the new rules derived from those.
P
|
Q
|
P→Q
|
P^Q
|
PvQ
|
(P^Q)→P
|
P ↔
Q
|
T
|
T
|
T
|
T
|
T
|
T
|
T
|
F
|
T
|
T
|
F
|
T
|
T
|
F
|
T
|
F
|
F
|
F
|
T
|
T
|
F
|
F
|
F
|
T
|
F
|
F
|
T
|
T
|
This is just a
simple introduction to propositional calculus, it is part of a much
broader branch of propositional logic . It is useful in the
formulation of logic rules, and methods of proof.
