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In logic, a logical connective (also truth-functional connective, logical operator or propositional operator) is a name for operators using which we form a compound proposition from one or two other propositions. The truth value of the resultant compound proposition is determined by the truth-value(s) of the composed proposition(s).
The basic logical connectives are:
Certain compound propositions have the same have logical content.(i.e. are logically equivalent). For instance, the compound propositions and
have the following truth tables:
This means that the logical connective can be replaced by
and
. From similar reasons a concept of functionally completeness is introduced. A set
of logical connectives is called functionally complete if every possible logical connective can be defined in terms of the connectives from
. Moreover,
is minimal functionally complete if no proper subset of
can be defined in terms of the other members of
. For instance
is a minimal functionally complete set of logical connectives. Here
is logically equivalent to
, and
to
(according to De Morgan Law) an the latest to
.
Cite this web-page as:
Štefan Porubský: Logical connectives.