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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.
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used to connect logical formulas. Connectives can be used to connect logical formulas.
Venn diagram of . Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional.
The logical disjunction operator thus usually constitutes a sequence point. In a parallel (concurrent) language, it is possible to short-circuit both sides: they are evaluated in parallel, and if one terminates with value true, the other is interrupted. This operator is thus called the parallel or.
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
Logical equivalence is different from material equivalence. Formulas and are logically equivalent if and only if the statement of their material equivalence is a tautology.
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 Neg row shows the operator op2 such that P op Q = ¬(P op2 Q). The Dual row shows the dual operation obtained by interchanging T with F, and AND with OR. The L id row shows the operator's left identities if it has any - values I such that I op Q = Q. The R id row shows the operator's right identities if it has any - values I such that P op ...