1. Prepared by:Nathaniel T. SullanoBS Math 3

2. is a science that deals with the principlesand criteria of validity of inference anddemonstration. is the formal systematic study ofthe principles of valid inference andcorrect reasoning. Logic is used in most intellectualactivities, but is studied primarily in thedisciplinesof philosophy, mathematics, semantics,and computer science.

3. has became mathematized in the 19th century, in thework of mostly British mathematicians such as GeorgePeacock (1791-1858), George Boole (1815-1864),William Stanley Jevons (1835-1882), and Augustus deMorgan, and a few Americans, notably Charles SandersPeirce. was the creation of 19th-century analysts and geometers,prominent among them is Georg Cantor (1845-1918),whose inspiration came from geometry and analysis,mostly the latter. mathematization of logic has a pre-history that goesback to Leibniz.

4. His main contribution to mathematical analysis is his attempt to place algebra on a strictly logical basis. Concluded that the science of algebra has two parts arithmetical and symbolical algebra. 1791-1858

5. developed two laws of negation (disjunction & conjunction) interested, like other mathematicians, in using mathematics to demonstrate logic furthered Booles work of incorporating logic and mathematics 1806-1871 formally stated the laws of set theory

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7. Lagranges algebraic approach to analysis (Thinking of Taylors Theorem).Where Df(x) = f(x), and comparing with the Taylors series of theexponential function, Lagrange arrived at the formal equation Converse relation,

8. self-taught mathematician with an interest in logic developed an algebra of logic (Boolean Algebra) featured the operators and or not nor (exclusive or) 1815-1864

9. Boole soon began to see the He wrote that,possibilities for applying his the validity of thealgebra to the solution of processes of analysislogical problems. Booles does not depend upon1847 work, The the interpretation of theMathematical Analysis of symbols which areLogic, not only expanded employed but solely uponon Gottfried Leibniz earlier the laws of theirspeculations on the combinationcorrelation between logicand math, but argued thatlogic was principally adiscipline of mathematics,rather than philosophy.

10. Boole denoted a generic member of a class by an uppercase X, and used the lowercase x. Then xy was to denote the class whose members are both Xs and Ys This language rather blurs the distinction between a set, its members, and the properties that determine what the members are.

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