. . . . . . . "Logical biconditional"@en . . . . . . . . . . . . . . . . "Bikonditional"@de . . . . . . . . . . "484"^^ . . . "Als Bikonditional, Bisubjunktion oder materiale \u00C4quivalenz, manchmal (aber mehrdeutig) einfach nur \u00C4quivalenz bezeichnet man \n* eine zusammengesetzte Aussage, die genau dann wahr ist, wenn ihre beiden Teilaussagen denselben Wahrheitswert haben, also entweder beide wahr oder beide falsch sind; \n* die entsprechend definierte Wahrheitswertfunktion; \n* das sprachliche Zeichen (den Junktor), mit dem diese beiden Teilaussagen zusammengesetzt werden."@de . . . . . "In logic and mathematics, the logical biconditional, sometimes known as the material biconditional, is the logical connective used to conjoin two statements P and Q to form the statement \"P if and only if Q\", where P is known as the antecedent, and Q the consequent. This is often abbreviated as \"P iff Q\". Other ways of denoting this operator may be seen occasionally, as a double-headed arrow (\u2194 or \u21D4 may be represented in Unicode in various ways), a prefixed E \"Epq\" (in \u0141ukasiewicz notation or Boche\u0144ski notation), an equality sign (=), an equivalence sign (\u2261), or EQV. It is logically equivalent to both and , and the XNOR (exclusive nor) boolean operator, which means \"both or neither\"."@en . . . . . . "Biconditional"@en . . . . . . . . "Na L\u00F3gica e Matem\u00E1tica, a L\u00F3gica bicondicional (tamb\u00E9m conhecida como bicondicional material) \u00E9 o Conectivo l\u00F3gico de duas proposi\u00E7\u00F5es afirmando \"p se e somente se q\", onde q \u00E9 uma Hip\u00F3tese (ou antecedente) e p \u00E9 um conclus\u00E3o (ou consequente). Isso \u00E9 frequentemente abreviado p sse q. O operador \u00E9 denotado usando uma seta de dupla implica\u00E7\u00E3o (\u2194), a prefixed E (Epq), um sinal de igualdade (=),um sinal de equival\u00EAncia (\u2261), ou EQV. Isso \u00E9 logicamente equivalente a (p \u2192 q) \u2227 (q \u2192 p), ou o XNOR (nor exclusivo) operador da \u00C1lgebra_booleana.Isto \u00E9 equivalente a \"(n\u00E3o p ou q) e (n\u00E3o q ou p)\". Tamb\u00E9m \u00E9 logicamente equivalente a \"(p e q) ou (n\u00E3o p e n\u00E3o q)\",significando \"os dois ou nenhum\".A \u00FAnica diferen\u00E7a paraCondicional_material \u00E9 o caso no qual a hip\u00F3tese \u00E9 falsa mas a conclus\u00E3o \u00E9 verdadeira. Nes"@pt . . . . . . . . . . . . . . . "Conectivo l\u00F3gico bicondicional"@pt . . . . . "228783"^^ . . . . . . . . . . . . . . . . . . . . . . . . . "In logic and mathematics, the logical biconditional, sometimes known as the material biconditional, is the logical connective used to conjoin two statements P and Q to form the statement \"P if and only if Q\", where P is known as the antecedent, and Q the consequent. This is often abbreviated as \"P iff Q\". Other ways of denoting this operator may be seen occasionally, as a double-headed arrow (\u2194 or \u21D4 may be represented in Unicode in various ways), a prefixed E \"Epq\" (in \u0141ukasiewicz notation or Boche\u0144ski notation), an equality sign (=), an equivalence sign (\u2261), or EQV. It is logically equivalent to both and , and the XNOR (exclusive nor) boolean operator, which means \"both or neither\". Semantically, the only case where a logical biconditional is different from a material conditional is the case where the hypothesis is false but the conclusion is true. In this case, the result is true for the conditional, but false for the biconditional. In the conceptual interpretation, P = Q means \"All P's are Q's and all Q's are P's\". In other words, the sets P and Q coincide: they are identical. However, this does not mean that P and Q need to have the same meaning (e.g., P could be \"equiangular trilateral\" and Q could be \"equilateral triangle\"). When phrased as a sentence, the antecedent is the subject and the consequent is the predicate of a universal affirmative proposition (e.g., in the phrase \"all men are mortal\", \"men\" is the subject and \"mortal\" is the predicate). In the propositional interpretation, means that P implies Q and Q implies P; in other words, the propositions are logically equivalent, in the sense that both are either jointly true or jointly false. Again, this does not mean that they need to have the same meaning, as P could be \"the triangle ABC has two equal sides\" and Q could be \"the triangle ABC has two equal angles\". In general, the antecedent is the premise, or the cause, and the consequent is the consequence. When an implication is translated by a hypothetical (or conditional) judgment, the antecedent is called the hypothesis (or the condition) and the consequent is called the thesis. A common way of demonstrating a biconditional of the form is to demonstrate that and separately (due to its equivalence to the conjunction of the two converse conditionals). Yet another way of demonstrating the same biconditional is by demonstrating that and . When both members of the biconditional are propositions, it can be separated into two conditionals, of which one is called a theorem and the other its reciprocal. Thus whenever a theorem and its reciprocal are true, we have a biconditional. A simple theorem gives rise to an implication, whose antecedent is the hypothesis and whose consequent is the thesis of the theorem. It is often said that the hypothesis is the sufficient condition of the thesis, and that the thesis is the necessary condition of the hypothesis. That is, it is sufficient that the hypothesis be true for the thesis to be true, while it is necessary that the thesis be true if the hypothesis were true. When a theorem and its reciprocal are true, its hypothesis is said to be the necessary and sufficient condition of the thesis. That is, the hypothesis is both the cause and the consequence of the thesis at the same time."@en . . . . . . . . . "Als Bikonditional, Bisubjunktion oder materiale \u00C4quivalenz, manchmal (aber mehrdeutig) einfach nur \u00C4quivalenz bezeichnet man \n* eine zusammengesetzte Aussage, die genau dann wahr ist, wenn ihre beiden Teilaussagen denselben Wahrheitswert haben, also entweder beide wahr oder beide falsch sind; \n* die entsprechend definierte Wahrheitswertfunktion; \n* das sprachliche Zeichen (den Junktor), mit dem diese beiden Teilaussagen zusammengesetzt werden."@de . . . . . "1123976069"^^ . . . . . . "Na L\u00F3gica e Matem\u00E1tica, a L\u00F3gica bicondicional (tamb\u00E9m conhecida como bicondicional material) \u00E9 o Conectivo l\u00F3gico de duas proposi\u00E7\u00F5es afirmando \"p se e somente se q\", onde q \u00E9 uma Hip\u00F3tese (ou antecedente) e p \u00E9 um conclus\u00E3o (ou consequente). Isso \u00E9 frequentemente abreviado p sse q. O operador \u00E9 denotado usando uma seta de dupla implica\u00E7\u00E3o (\u2194), a prefixed E (Epq), um sinal de igualdade (=),um sinal de equival\u00EAncia (\u2261), ou EQV. Isso \u00E9 logicamente equivalente a (p \u2192 q) \u2227 (q \u2192 p), ou o XNOR (nor exclusivo) operador da \u00C1lgebra_booleana.Isto \u00E9 equivalente a \"(n\u00E3o p ou q) e (n\u00E3o q ou p)\". Tamb\u00E9m \u00E9 logicamente equivalente a \"(p e q) ou (n\u00E3o p e n\u00E3o q)\",significando \"os dois ou nenhum\".A \u00FAnica diferen\u00E7a paraCondicional_material \u00E9 o caso no qual a hip\u00F3tese \u00E9 falsa mas a conclus\u00E3o \u00E9 verdadeira. Neste caso, na condicional, o resultado \u00E9 verdadeiro, contudo, na bicondicional o resultado \u00E9 falso.Na interpreta\u00E7\u00E3o conceitual, a = b significa \"Todos os a 's s\u00E3o b 's e todos os b 's s\u00E3o a 's\"; Em outras palavras, os conjuntos a e b coincidem: eles s\u00E3o id\u00EAnticos. Isso n\u00E3o significa que todos os conceitos t\u00EAm o mesmo significado. Exemplos: \"tri\u00E2ngulo\" e \"trilateral\", \"tri\u00E2ngulo equiangular\" e \"tri\u00E2ngulo equil\u00E1tero\". O antecedente \u00E9 o \"sujeito\" e o consequente \u00E9 o e predicado de uma afirmativa/ Proposi\u00E7\u00E3o universal. Na interpreta\u00E7\u00E3o proposicional, a \u21D4 b significa que a implica b e b implica a; em outras palavras, que as proposi\u00E7\u00F5es s\u00E3o equivalentes, o que \u00E9 dizer, ambas s\u00E3o verdadeiras ou falsas ao mesmo tempo. Isso n\u00E3o significa que elas tem o mesmo significado. Exemplo: \"O tri\u00E2ngulo ABC tem dois lados iguais\", e \"O tri\u00E2ngulo ABC tem 2 \u00E2ngulos iguais\". O antecedente \u00E9 a premissa ou a causa e o consequente \u00E9 a consequ\u00EAncia. Quando uma implica\u00E7\u00E3o \u00E9 traduzida por um julgamento hipot\u00E9tico (ou condicional) O antecedente \u00E9 chamado de \"hip\u00F3tese (ou de condi\u00E7\u00E3o) e o consequente \u00E9 chamado de tese. Uma forma comum de se demonstrar um bicondicional \u00E9 usar sua equival\u00EAncia para a conjun\u00E7\u00E3o de duas condicionais ,em que h\u00E1 uma troca entre a hip\u00F3tese e a conclus\u00E3o, as demonstrando separadamente."@pt . "16561"^^ . .