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The operator so characterized is often called De Morgan negation, for also De Morgan's Laws hold for it.

Then, being a supreme mathematical technician, he could dress it up, how you will, for purposes of exposition, but it was his intuition which was preeminently extraordinary – 'So happy in his conjectures,' said De Morgan, 'as to seem to know more than he could possibly have any means of proving.'

De Morgan wrote a series of six papers called “On the Syllogism” in the years 1846 to 1863.

After noting that McColl's accent allowed one to take the negation of complex bracketed terms he went on to say that, for the most part, he found the notation of De Morgan, the notation that he had always used, to be the more elegant.

Jevons, who had studied with De Morgan, was the first to offer an alternative to Boole's system.

Like De Morgan, Peirce also considered a number of other natural operations on relations.

De Morgan gets credit for introducing the concept of relations, but Peirce is considered the true creator of the theory of relations.

There are many different and wellworked out logical theories of negation (minimal negation, intuitionistic negation, De Morgan negation, etc.).

His work on relations building on ideas of De Morgan influenced Schroder, and through Schroder, Peano, Russell, Lowenheim and much of contemporary logical theory.

Building on ideas of De Morgan, Peirce fruitfully applied the concepts of Boolean algebra to relations.
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