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Conjunction/disjunction duality, the Glossary

In propositional logic and Boolean algebra, there is a duality between conjunction and disjunction, also called the duality principle.^[1]

19 relations: Boolean algebra, Classical logic, Conjunctive normal form, Contraposition, De Morgan's laws, Disjunctive normal form, Double negation, Functional completeness, Logical conjunction, Logical connective, Logical disjunction, Mathematical induction, Metalogic, Negation, Propositional calculus, Propositional variable, Q.E.D., Semantics of logic, Well-formed formula.
Logic symbols
Logical connectives

Boolean algebra

In mathematics and mathematical logic, Boolean algebra is a branch of algebra.

See Conjunction/disjunction duality and Boolean algebra

Classical logic

Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic.

See Conjunction/disjunction duality and Classical logic

In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs.

See Conjunction/disjunction duality and Conjunctive normal form

Contraposition

In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as.

See Conjunction/disjunction duality and Contraposition

De Morgan's laws

In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference.

See Conjunction/disjunction duality and De Morgan's laws

Disjunctive normal form

In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or in philosophical logic a cluster concept.

See Conjunction/disjunction duality and Disjunctive normal form

Double negation

In propositional logic, the double negation of a statement states that "it is not the case that the statement is not true".

See Conjunction/disjunction duality and Double negation

Functional completeness

In logic, a functionally complete set of logical connectives or Boolean operators is one that can be used to express all possible truth tables by combining members of the set into a Boolean expression.

See Conjunction/disjunction duality and Functional completeness

Logical conjunction

In logic, mathematics and linguistics, and (\wedge) is the truth-functional operator of conjunction or logical conjunction. Conjunction/disjunction duality and logical conjunction are logical connectives and semantics.

See Conjunction/disjunction duality and Logical conjunction

Logical connective

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Conjunction/disjunction duality and logical connective are logic symbols and logical connectives.

See Conjunction/disjunction duality and Logical connective

Logical disjunction

In logic, disjunction, also known as logical disjunction or logical or or logical addition or inclusive disjunction, is a logical connective typically notated as \lor and read aloud as "or". Conjunction/disjunction duality and logical disjunction are logical connectives and semantics.

See Conjunction/disjunction duality and Logical disjunction

Mathematical induction

Mathematical induction is a method for proving that a statement P(n) is true for every natural number n, that is, that the infinitely many cases P(0), P(1), P(2), P(3), \dots  all hold.

See Conjunction/disjunction duality and Mathematical induction

Metalogic is the metatheory of logic.

See Conjunction/disjunction duality and Metalogic

Negation

In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P to another proposition "not P", standing for "P is not true", written \neg P, \mathord P or \overline. Conjunction/disjunction duality and negation are logical connectives and semantics.

See Conjunction/disjunction duality and Negation

Propositional calculus

The propositional calculus is a branch of logic.

See Conjunction/disjunction duality and Propositional calculus

Propositional variable

In mathematical logic, a propositional variable (also called a sentence letter, sentential variable, or sentential letter) is an input variable (that can either be true or false) of a truth function. Conjunction/disjunction duality and propositional variable are logic symbols.

See Conjunction/disjunction duality and Propositional variable

Q.E.D.

Q.E.D. or QED is an initialism of the Latin phrase quod erat demonstrandum, meaning "that which was to be demonstrated".

See Conjunction/disjunction duality and Q.E.D.

Semantics of logic

In logic, the semantics of logic or formal semantics is the study of the semantics, or interpretations, of formal languages and (idealizations of) natural languages usually trying to capture the pre-theoretic notion of logical consequence. Conjunction/disjunction duality and semantics of logic are semantics.

See Conjunction/disjunction duality and Semantics of logic

Well-formed formula

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language.

See Conjunction/disjunction duality and Well-formed formula

References

[1] https://en.wikipedia.org/wiki/Conjunction/disjunction_duality

Also known as Duality principle (Boolean algebra).