Formal logic

Propositional calculus

Propositional calculus is the simplest and most basic branch of logic because the propositions are unanalysed.

The symbols used in propositional calculus are:

  • variables
  • operators
  • brackets


Variables, such as p, q and r represent unspecified propositions in formulas into which only sentences may be inserted.


Operators create a new proposition from one or more given propositions which are called the arguments of the operator.

The operators are:

Formal logic - operators


Brackets make it possible to distinguish, for example, between

Formal logic - brackets

In other words, the first proposition is “both p and either q or r”, and this differs in meaning to the second proposition “either both p and q or r”.

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