## Wednesday, July 1, 2015

### Propositional calculus: an introduction

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.