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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.
Here are numerical examples of some basic logical gates implemented as ... Then it can be proved that in the two-dimensional vector logic the De Morgan's law is a ...
This is commonly seen in real logic diagrams – thus the reader must not get into the habit of associating the shapes exclusively as OR or AND shapes, but also take into account the bubbles at both inputs and outputs in order to determine the "true" logic function indicated. A De Morgan symbol can show more clearly a gate's primary logical ...
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.
To investigate the left distributivity of set subtraction over unions or intersections, consider how the sets involved in (both of) De Morgan's laws are all related: () = = () always holds (the equalities on the left and right are De Morgan's laws) but equality is not guaranteed in general (that is, the containment might be strict).
By De Morgan's laws, a two-input NAND gate's logic may be expressed as ¯ ¯ = ¯, making a NAND gate equivalent to inverters followed by an OR gate. The NAND gate is significant because any Boolean function can be implemented by using a combination of NAND gates.
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An XNOR gate is made by considering the disjunctive normal form + ¯ ¯, noting from de Morgan's law that a NAND gate is an inverted-input OR gate. This construction entails a propagation delay three times that of a single NAND gate and uses five gates.