Search results
Results from the WOW.Com Content Network
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.
De Morgan algebras are important for the study of the mathematical aspects of fuzzy logic. The standard fuzzy algebra F = ([0, 1], max( x , y ), min( x , y ), 0, 1, 1 − x ) is an example of a De Morgan algebra where the laws of excluded middle and noncontradiction do not hold.
Boolean prime ideal theorem; Compactness theorem; Consensus theorem; De Morgan's laws; Duality (order theory) Laws of classical logic; Peirce's law; Stone's representation theorem for Boolean algebras
Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician.He is best known for De Morgan's laws, relating logical conjunction, disjunction, and negation, and for coining the term "mathematical induction", the underlying principles of which he formalized. [1]
The principle of inclusion–exclusion, combined with De Morgan's law, can be used to count the cardinality of the intersection of sets as well. Let A k ¯ {\displaystyle {\overline {A_{k}}}} represent the complement of A k with respect to some universal set A such that A k ⊆ A {\displaystyle A_{k}\subseteq A} for each k .
De Morgan's theorem states that if one does the following, in the given order, to any Boolean function: Complement every variable; Swap '+' and '∙' operators (taking care to add brackets to ensure the order of operations remains the same); Complement the result, the result is logically equivalent to what you started with. Repeated application ...
A De Morgan symbol can show more clearly a gate's primary logical purpose and the polarity of its nodes that are considered in the "signaled" (active, on) state. Consider the simplified case where a two-input NAND gate is used to drive a motor when either of its inputs are brought low by a switch.
De Bruijn–Erdős theorem: Mathematics: Nicolaas Govert de Bruijn and Paul Erdős: De Morgan's law: Logic: Augustus De Morgan: Dermott's law: Celestial mechanics: Stanley Dermott: Descartes's theorem: Geometry: René Descartes: Dirac equation Dirac delta function Dirac comb Dirac spinor Dirac operator See also: List of things named after Paul ...