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The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), [2] and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of ...
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or bidirectional implication or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.
Some authors used letters for connectives: . for conjunction (German's "und" for "and") and . for disjunction (German's "oder" for "or") in early works by Hilbert (1904); [16] for negation, for conjunction, for alternative denial, for disjunction, for implication, for biconditional in Łukasiewicz in 1929.
material biconditional (material equivalence) if and only if, iff, xnor propositional logic, Boolean algebra: is true only if both A and B are false, or both A and B are true. Whether a symbol means a material biconditional or a logical equivalence, depends on the author’s style.
[35] [36] In English, these connectives are expressed by the words "and" (conjunction), "or" (disjunction), "not" , "if" (material conditional), and "if and only if" (biconditional). [1] [13] Examples of such compound sentences might include: Wikipedia is a free online encyclopedia that anyone can edit, and millions already have. (conjunction)
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 ∧ {\displaystyle \wedge } [ 1 ] or & {\displaystyle \&} or K {\displaystyle K} (prefix) or × {\displaystyle \times } or ⋅ {\displaystyle \cdot } [ 2 ] in ...
In logic, the term conditional disjunction can refer to: conditioned disjunction , a ternary logical connective introduced by Alonzo Church a rule in classical logic that the material conditional ¬ p → q is equivalent to the disjunction p ∨ q , so that these two formulae are interchangeable - see Negation
Logical connectives: ∧ for conjunction, ∨ for disjunction, → for implication, ↔ for biconditional, ¬ for negation. Some authors [11] use Cpq instead of → and Epq instead of ↔, especially in contexts where → is used for other purposes.