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De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form , [1] minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF ), maxterm canonical form , or Product of Sums ( PoS or POS ) which is a ...
A Boolean algebra is a set A, equipped with two binary operations ∧ (called "meet" or "and"), ∨ (called "join" or "or"), a unary operation ¬ (called "complement" or "not") and two elements 0 and 1 in A (called "bottom" and "top", or "least" and "greatest" element, also denoted by the symbols ⊥ and ā¤, respectively), such that for all elements a, b and c of A, the following axioms hold: [2]
Corner quotes, also called “Quine quotes”; for quasi-quotation, i.e. quoting specific context of unspecified (“variable”) expressions; [3] also used for denoting Gödel number; [4] for example “āGā” denotes the Gödel number of G. (Typographical note: although the quotes appears as a “pair” in unicode (231C and 231D), they ...
A law of Boolean algebra is an identity such as x ∨ (y ∨ z) = (x ∨ y) ∨ z between two Boolean terms, where a Boolean term is defined as an expression built up from variables and the constants 0 and 1 using the operations ∧, ∨, and ¬. The concept can be extended to terms involving other Boolean operations such as ⊕, →, and ≡ ...
In Boolean functions, each separate occurrence of a variable, either in inverse or uncomplemented form, is a literal. For example, if A {\displaystyle A} , B {\displaystyle B} and C {\displaystyle C} are variables then the expression A ¯ B C {\displaystyle {\bar {A}}BC} contains three literals and the expression A ¯ C + B ¯ C ...
The POS expression gives a complement of the function (if F is the function so its complement will be F'). [10] Karnaugh maps can also be used to simplify logic expressions in software design. Boolean conditions, as used for example in conditional statements , can get very complicated, which makes the code difficult to read and to maintain.
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [ 1 ] [ 2 ] Alternative names are switching function , used especially in older computer science literature, [ 3 ] [ 4 ] and truth function (or logical function) , used in logic .