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Conjunction Both A and B conjunct A and B are conjoined Disjunction Either A or B, or both disjunct A and B are disjoined Negation It is not the case that A negatum/negand A is negated Conditional If A, then B antecedent, consequent B is implied by A Biconditional A if, and only if, B equivalents A and B are equivalent
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.
[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 propositional logic and Boolean algebra, there is a duality between conjunction and disjunction, [1] [2] [3] also called the duality principle. [ 4 ] [ 5 ] [ 6 ] It is the most widely known example of duality in logic. [ 1 ]
De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.
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 ...
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