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In Boolean logic, logical NOR, [1] non-disjunction, or joint denial [1] is a truth-functional operator which produces a result that is the negation of logical or.That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both p and q are false.
[2] [3] Peirce's editor added ¯) for non-disjunction [citation needed]. [ 3 ] In 1911, Stamm was the first to publish a proof of the completeness of non-conjunction, representing this with ∼ {\displaystyle \sim } (the Stamm hook ) [ 4 ] and non-disjunction in print at the first time and showed their functional completeness.
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
For example, RAID can "back up" bytes 10011100 2 and 01101100 2 from two (or more) hard drives by XORing the just mentioned bytes, resulting in (11110000 2) and writing it to another drive. Under this method, if any one of the three hard drives are lost, the lost byte can be re-created by XORing bytes from the remaining drives.
Disjunction: the symbol appeared in Russell in 1908 [5] (compare to Peano's use of the set-theoretic notation of union); the symbol + is also used, in spite of the ambiguity coming from the fact that the + of ordinary elementary algebra is an exclusive or when interpreted logically in a two-element ring; punctually in the history a + together ...
First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather than propositions such as "all men are mortal", in first-order logic one can have expressions in the form "for all x, if x is a man, then x is mortal"; where "for all x" is a quantifier, x is a variable, and "...
A function or mapping from one set to another where every element of the second set is associated with at least one element of the first set; also known as surjective. open formula A formula in a formal language that contains free variables, meaning it cannot be determined as true or false until the variables are bound or specified. open pair
A logical formula is considered to be in CNF if it is a conjunction of one or more disjunctions of one or more literals. As in disjunctive normal form (DNF), the only propositional operators in CNF are or ( ∨ {\displaystyle \vee } ), and ( ∧ {\displaystyle \wedge } ), and not ( ¬ {\displaystyle \neg } ).