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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 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.
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.
Logical biconditional; Logical equality; ≡ the iff symbol (U+2261 IDENTICAL TO) ∷ the a is to b as c is to d symbol (U+2237 PROPORTION) ⇔ the double struck biconditional (U+21D4 LEFT RIGHT DOUBLE ARROW) ↔ the bidirectional arrow (U+2194 LEFT RIGHT ARROW)
The symbol for material implication signifies the proposition as a hypothetical, or the "if–then" form, e.g. "if P, then Q". The biconditional statement of the rule of transposition (↔) refers to the relation between hypothetical (→) propositions , with each proposition including an antecedent and consequential term.
Biconditional introduction / elimination; ... " is a metalogical symbol representing "can be replaced in a proof with", P and Q are any given logical statements, ...
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 symbol ≡ is used in science and mathematics with several different meanings. It may refer to the following: ... Logical biconditional, in logic (if and only if ...