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Logical connectives

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:

• negation read “not” , written or ~
• conjunction read  “and”, written or
• disjunction read “or”, written or
• implication  read “if...then”, written , or
• equivalence or biconditional  read “if and only if”  or  “xnor”, written , or

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 .

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