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Discrete Mathematics with Graph Theory (3rd Edition) 23

Discrete Mathematics with Graph Theory (3rd Edition) 23 -...

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Section 1.3 21 never a Fellow of the Royal Society because he refused to let his name be put forward and, similarly, refused an honorary degree from.the University of Edinburgh. De Morgan's mathematical contributions include the definition and introduction of "mathematical in- duction", the most important method of proof in mathematics today. See Section 5.1. His definition of a limit was the first attempt to define the idea in precise mathematical terms. Nonetheless, it is the area of mathematical logic with which De Morgan's name is most closely associated. The "Laws of De Morgan" introduced in this section, together with their set theoretical analogues-(AUBY = AcnB c , (A n B)C = AC U BC (see Section 2.2)-are used extensively and of fundamental importance. De Morgan also developed a system of notation for symbolic logic that could denote converses and con- tradictions. Exercises 1.3 1. (a) [BB]Since[p-+(q-+r)] ¢::::::> [p-+((-,q)Vr)] ¢::::::> [(-,p)V(-,q)Vr],thegivenargument can be rewritten which is valid by disjunctive syllogism.
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