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Augustus De Morgan (1806-1871) |
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Proposal Number Sense Interactive Quiz Lesson Plans History Problem Bank Glossary Quotes Helpful Links References
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His main accomplishments were
in the field of logic, although he studied both probability and algebra.
He wrote a series of textbooks on arithmetic, algebra,
trigonometry, calculus, complex numbers, probability, and logic.
He is known for the development of De Morgan’s Laws, which deal
with the logic of relations. This
means that "all statements had to be analyzed into the form ‘A is
(or is not) B,’ with the possible inclusion of ‘all’ and
‘some’" (Young, 1998, p. 143).
For example, the first law states that the negation of the
statement "P and Q" is equivalent to the statement "not P
or Q" (Smith, 1996, p. 137). The
second law states that the negation of the statement "P or Q"
is equivalent to the statement "not P and not Q" (Smith, 1996,
p. 137).
He died in 1871, having created
new ideas for other mathematicians to examine and ponder.
Additional
Links:
Activity
#5: De
Morgan’s laws, stated in terms of sets, are shown below.
Use the Venn diagrams given below to demonstrate the equivalency
of the indicated sets. (The notation A’ refers to the complement of A;
that is, all elements not in the set A.) Link to solution. Picture reproduced from MacTutor History of Mathematics archive with permission. |
