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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
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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