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biconditional

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Definitions of biconditional in various dictionaries:

BICONDITIONAL - In logic and mathematics, the logical biconditional (sometimes known as the material biconditional) is the logical connective of two statements asser...

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Possible Dictionary Clues
Having two conditions
An "if and only if" conditional wherein the truth of each term depends on the truth of the other

Biconditional might refer to
In logic and mathematics, the Logical biconditional (sometimes known as the material biconditional) is the logical connective of two statements asserting " * * * * P * * * {\displaystyle P} * if and only if * * * * Q * * * {\displaystyle Q} * ", where * * * * P * * * {\displaystyle P} * is an antecedent and * * * * Q * * * {\displaystyle Q} * is a consequent. This is often abbreviated " * * * * P * * * {\displaystyle P} * iff * * * * Q * * * {\displaystyle Q} * ". The operator is denoted using a doubleheaded arrow (↔), a prefixed E "Epq" (in Łukasiewicz notation or Bocheński notation), an equality sign (=), an equivalence sign (≡), or EQV. It is logically equivalent to * * * * ( * P * → * Q * ) * ∧ * ( * Q * → * P * ) * * * {\displaystyle (P\rightarrow Q)\land (Q\rightarrow P)} * and to * * * * ( * P * ∧ * Q * ) * ∨ * ( * ¬ * P * ∧ * ¬ * Q * ) * * * {\displaystyle (P\land Q)\lor (\neg P\land \neg Q)} * (or the XNOR (exclusive nor) boolean operator), 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, * * * * P * = * Q * * * {\displaystyle P=Q} * means "All * * * * P * * * {\displaystyle P} * 's are * * * * Q * * * {\displaystyle Q} * 's and all ' * * * * Q * * * {\displaystyle Q} * 's are * * * * P * * * {\displaystyle P} * 's"; in other words, the sets * * * * P * * * {\displaystyle P} * and * * * * Q * * * {\displaystyle Q} * 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, * * * * P * ⇔ * Q * * * {\displaystyle P\Leftrightarrow Q} * (⇔) means that * * * * P * * * {\displaystyle P} * implies * * * * Q * * * {\displaystyle Q} * and * * * * Q * * * {\displaystyle Q} * implies * * * * P * * * {\displaystyle P} * ; 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 h...

Biconditional might refer to

In logic and mathematics, the Logical biconditional (sometimes known as the material biconditional) is the logical connective of two statements asserting "
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* is an antecedent and
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* is a consequent. This is often abbreviated "
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* iff
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* ". The operator is denoted using a doubleheaded arrow (↔), a prefixed E "Epq" (in Łukasiewicz notation or Bocheński notation), an equality sign (=), an equivalence sign (≡), or EQV. It is logically equivalent to
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* and to
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* {\displaystyle (P\land Q)\lor (\neg P\land \neg Q)}
* (or the XNOR (exclusive nor) boolean operator), 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,
*
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* P
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* Q
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* {\displaystyle P=Q}
* means "All
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* 's are
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* 's and all '
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* 's are
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* 's"; in other words, the sets
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* 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,
*
*
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* P
* ⇔
* Q
*
*
* {\displaystyle P\Leftrightarrow Q}
* (⇔) means that
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* implies
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* and
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* implies
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* ; 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 h...

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