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In logic, disjunction, also known as logical disjunction or logical or or logical addition or inclusive disjunction, is a logical connective typically notated as and read aloud as "or".
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
The symbol used for exclusive disjunction varies from one field of application to the next, and even depends on the properties being emphasized in a given context of discussion. In addition to the abbreviation "XOR", any of the following symbols may also be seen: + was used by George Boole in 1847. [6]
Disjunction: the symbol appeared in Russell in 1908 [6] (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 ...
Venn diagram for "A or B", with inclusive or (OR) Venn diagram for "A or B", with exclusive or (XOR). The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true because "or" is defined inclusively rather than exclusively.
A logical formula is considered to be in DNF if it is a disjunction of one or more conjunctions of one or more literals. [2] [3] [4] A DNF formula is in full disjunctive normal form if each of its variables appears exactly once in every conjunction and each conjunction appears at most once (up to the order of variables).
In addition to 1 and 0, these states may be called true and false, high and low, active and inactive, or other such pairs of symbols. Thus it performs a logical disjunction (∨) from mathematical logic. The gate can be represented with the plus sign (+) because it can be used for logical addition. [1]
An equality symbol (sometimes, identity symbol) = (see § Equality and its axioms below). Not all of these symbols are required in first-order logic. Either one of the quantifiers along with negation, conjunction (or disjunction), variables, brackets, and equality suffices. Other logical symbols include the following: