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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 a hypothesis (or antecedent) and p is a conclusion (or 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 triangle" 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.[citation needed] 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.".
- Logical_biconditional thumbnail Multigrade_operator_XNOR.svg?width=300.
- Logical_biconditional wikiPageExternalLink 1up.
- Logical_biconditional wikiPageID "228783".
- Logical_biconditional wikiPageRevisionID "602608704".
- Logical_biconditional hasPhotoCollection Logical_biconditional.
- Logical_biconditional id "484".
- Logical_biconditional title "Biconditional".
- Logical_biconditional subject Category:Logical_connectives.
- Logical_biconditional type Abstraction100002137.
- Logical_biconditional type Conjunction106325826.
- Logical_biconditional type FunctionWord106291318.
- Logical_biconditional type LanguageUnit106284225.
- Logical_biconditional type LogicalConnectives.
- Logical_biconditional type Part113809207.
- Logical_biconditional type Relation100031921.
- Logical_biconditional type Word106286395.
- 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 a hypothesis (or antecedent) and p is a conclusion (or 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.".
- Logical_biconditional label "Bikonditional".
- Logical_biconditional label "Conectivo lógico bicondicional".
- Logical_biconditional label "Logical biconditional".
- Logical_biconditional sameAs Bikonditional.
- Logical_biconditional sameAs Conectivo_lógico_bicondicional.
- Logical_biconditional sameAs m.01h9m5.
- Logical_biconditional sameAs Q204355.
- Logical_biconditional sameAs Q204355.
- Logical_biconditional sameAs Logical_biconditional.
- Logical_biconditional wasDerivedFrom Logical_biconditional?oldid=602608704.
- Logical_biconditional depiction Multigrade_operator_XNOR.svg.
- Logical_biconditional isPrimaryTopicOf Logical_biconditional.
