# Definitions for deductive closurede·duc·tive clo·sure

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1. deductive closurenoun

The set of all the statements that can be deduced from a given set of statements.

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1. Deductive closure

Deductive closure is a property of a set of objects. A set of objects, O, is said to exhibit closure or to be closed under a given operation, R, provided that for every object, x, if x is a member of O and x is R-related to any object, y, then y is a member of O. In the context of statements, a deductive closure is the set of all the statements that can be deduced from a given set of statements. In propositional logic, the set of all true propositions exhibits deductive closure: if set O is the set of true propositions, and operation R is logical consequence, then provided that proposition p is a member of O and p is R-related to q, q is also a member of O.

### Numerology

1. Chaldean Numerology

The numerical value of deductive closure in Chaldean Numerology is: 4

2. Pythagorean Numerology

The numerical value of deductive closure in Pythagorean Numerology is: 6

## Translations for deductive closure

### From our Multilingual Translation Dictionary

• deduktiver Verschluss

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"deductive closure." Definitions.net. STANDS4 LLC, 2022. Web. 29 Jan. 2022. <https://www.definitions.net/definition/deductive+closure>.

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