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Venn diagram of . In logic, mathematics and linguistics, and is the truth-functional operator of conjunction or logical conjunction.The logical connective of this operator is typically represented as [1] or & or (prefix) or or [2] in which is the most modern and widely used.
Logical connectives can be used to link zero or more statements, so one can speak about n-ary logical connectives. The boolean constants True and False can be thought of as zero-ary operators. Negation is a unary connective, and so on.
Due to the ability to speak about non-logical individuals along with the original logical connectives, first-order logic includes propositional logic. [ 7 ] : 29–30 The truth of a formula such as " x is a philosopher" depends on which object is denoted by x and on the interpretation of the predicate "is a philosopher".
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false).
Pages in category "Logical connectives" The following 21 pages are in this category, out of 21 total. ... Logical conjunction; Converse (logic) Converse ...
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
The connectives are usually taken to be logical constants, meaning that the meaning of the connectives is always the same, independent of what interpretations are given to the other symbols in a formula. This is how we define logical connectives in propositional logic: ¬Φ is True iff Φ is False. (Φ ∧ Ψ) is True iff Φ is True and Ψ is True.
The following are the most common defined logical connectives: Weak conjunction (binary), also called lattice conjunction (as it is always realized by the lattice operation of meet in algebraic semantics). Unlike MTL and weaker substructural logics, weak conjunction is definable in BL as