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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.
Logic gate; Boolean analysis; Theorems and specific laws. Boolean prime ideal theorem; Compactness theorem; Consensus theorem; De Morgan's laws; Duality (order theory)
A logic gate is a device that performs a Boolean function, ... De Morgan's theorem is most commonly used to implement logic gates as combinations of only NAND gates ...
De Morgan's laws: In propositional logic and Boolean algebra, De Morgan's laws, [15] [16] [17] also known as De Morgan's theorem, [18] are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician.
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.
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]
Löb's theorem A theorem in mathematical logic that provides conditions under which a statement about its own provability is provable, related to Gödel's incompleteness theorems. logic The systematic study of the form of valid inference, including the structures that allow or compel particular conclusions given certain premises. logic gate
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. [1]