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- Logical_biconditional abstract "In logic and mathematics, the logical biconditional (sometimes known as the material biconditional) is the logical connective of two statements asserting "p if and only if q", where q is an antecedent and p is a consequent. This is often abbreviated p iff q. The operator is denoted using a doubleheaded arrow (↔), a prefixed E (Epq), an equality sign (=), an equivalence sign (≡), or EQV. It is logically equivalent to (p → q) ∧ (q → p), or the XNOR (exclusive nor) boolean operator. It is equivalent to "(not p or q) and (not q or p)". It is also logically equivalent to "(p and q) or (not p and not q)", meaning "both or neither".The only difference from material conditional is the case when the hypothesis is false but the conclusion is true. In that case, in the conditional, the result is true, yet in the biconditional the result is false.In the conceptual interpretation, a = b means "All a 's are b 's and all b 's are a 's"; in other words, the sets a and b coincide: they are identical. This does not mean that the concepts have the same meaning. Examples: "triangle" and "trilateral", "equiangular trilateral" and "equilateral triangle". The antecedent is the subject and the consequent is the predicate of a universal affirmative proposition.In the propositional interpretation, a ⇔ b means that a implies b and b implies a; in other words, that the propositions are equivalent, that is to say, either true or false at the same time. This does not mean that they have the same meaning. Example: "The triangle ABC has two equal sides", and "The triangle ABC has two equal angles". 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 is to use its equivalence to the conjunction of two converse conditionals, demonstrating these separately.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 thethesis the necessary condition of the hypothesis; that is to say, it is sufficient that the hypothesis be true for the thesis to be true; while it is necessary that the thesis be true for the hypothesis to be true also. When a theorem and its reciprocal are true we say that its hypothesis is the necessary and sufficient condition of the thesis; that is to say, that it is at the same time both cause and consequence.".
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- Logical_biconditional wikiPageWikiLink Antecedent_(logic).
- Logical_biconditional wikiPageWikiLink Associative_property.
- Logical_biconditional wikiPageWikiLink Associativity.
- Logical_biconditional wikiPageWikiLink Biconditional_elimination.
- Logical_biconditional wikiPageWikiLink Biconditional_introduction.
- Logical_biconditional wikiPageWikiLink Categorical_proposition.
- Logical_biconditional wikiPageWikiLink Category:Logical_connectives.
- Logical_biconditional wikiPageWikiLink Commutative_property.
- Logical_biconditional wikiPageWikiLink Commutativity.
- Logical_biconditional wikiPageWikiLink Consequent.
- Logical_biconditional wikiPageWikiLink Distributive_property.
- Logical_biconditional wikiPageWikiLink Distributivity.
- Logical_biconditional wikiPageWikiLink Exclusive_or.
- Logical_biconditional wikiPageWikiLink Hadamard_transform.
- Logical_biconditional wikiPageWikiLink Harper_&_Row.
- Logical_biconditional wikiPageWikiLink Harper_(publisher).
- Logical_biconditional wikiPageWikiLink Idempotence.
- Logical_biconditional wikiPageWikiLink Idempotency.
- Logical_biconditional wikiPageWikiLink If_and_only_if.
- Logical_biconditional wikiPageWikiLink Linear.
- Logical_biconditional wikiPageWikiLink Linearity.
- Logical_biconditional wikiPageWikiLink Logic.
- Logical_biconditional wikiPageWikiLink Logical_connective.
- Logical_biconditional wikiPageWikiLink Logical_disjunction.
- Logical_biconditional wikiPageWikiLink Logical_equality.
- Logical_biconditional wikiPageWikiLink Logical_equivalence.
- Logical_biconditional wikiPageWikiLink Logical_operation.
- Logical_biconditional wikiPageWikiLink Logical_value.
- Logical_biconditional wikiPageWikiLink Material_conditional.
- Logical_biconditional wikiPageWikiLink Mathematics.
- Logical_biconditional wikiPageWikiLink Monotone_boolean_function.
- Logical_biconditional wikiPageWikiLink Monotonic_function.
- Logical_biconditional wikiPageWikiLink Necessary_and_sufficient_condition.
- Logical_biconditional wikiPageWikiLink Necessary_condition.
- Logical_biconditional wikiPageWikiLink Necessity_and_sufficiency.
- Logical_biconditional wikiPageWikiLink Negation.
- Logical_biconditional wikiPageWikiLink Pons_asinorum.
- Logical_biconditional wikiPageWikiLink Proposition.
- Logical_biconditional wikiPageWikiLink Sufficient_condition.
- Logical_biconditional wikiPageWikiLink Truth_value.
- Logical_biconditional wikiPageWikiLink Universal_affirmative.
- Logical_biconditional wikiPageWikiLink XNOR_gate.
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- Logical_biconditional wikiPageWikiLinkText "Biconditional (XNOR, )".
- Logical_biconditional wikiPageWikiLinkText "Biconditional (if and only if)".
- Logical_biconditional wikiPageWikiLinkText "Biconditional (if and only if, xnor)".
- Logical_biconditional wikiPageWikiLinkText "Biconditional".
- Logical_biconditional wikiPageWikiLinkText "Logical biconditional".
- Logical_biconditional wikiPageWikiLinkText "XNOR".
- Logical_biconditional wikiPageWikiLinkText "biconditional".
- Logical_biconditional wikiPageWikiLinkText "biconditionals".
- Logical_biconditional wikiPageWikiLinkText "equivalence".
- Logical_biconditional wikiPageWikiLinkText "logical biconditional".
- Logical_biconditional wikiPageWikiLinkText "material biconditional".
- Logical_biconditional hasPhotoCollection Logical_biconditional.
- Logical_biconditional id "484".
- Logical_biconditional title "Biconditional".
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- Logical_biconditional subject Category:Logical_connectives.
- Logical_biconditional hypernym Antecedent.
- Logical_biconditional type Article.
- Logical_biconditional type PoliticalParty.
- Logical_biconditional type Article.
- Logical_biconditional type Source.
- Logical_biconditional comment "In logic and mathematics, the logical biconditional (sometimes known as the material biconditional) is the logical connective of two statements asserting "p if and only if q", where q is an antecedent and p is a consequent. This is often abbreviated p iff q. The operator is denoted using a doubleheaded arrow (↔), a prefixed E (Epq), an equality sign (=), an equivalence sign (≡), or EQV. It is logically equivalent to (p → q) ∧ (q → p), or the XNOR (exclusive nor) boolean operator.".
- Logical_biconditional label "Logical biconditional".
- Logical_biconditional sameAs Bikonditional.
- Logical_biconditional sameAs دوشرطی_منطقی.
- Logical_biconditional sameAs שקילות_(לוגיקה).
- Logical_biconditional sameAs Логички_двоуслов.