IST4_lec8

IST4_lec8 - IST 4 Information and Logic IST 4: Planned...

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IST 4 Information and Logic
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1 M1 31 6 2 6 5 26 19 M2 5 4 12 4 5 3 M2 28 3 2 21 2 1 14 M1 7 fri thr wed tue mon IST 4: Planned Schedule – Spring 2008 x= hw#x out x= hw#x due = today T Mx= MQx out Mx= MQx due midterms midterms T
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The Algebra (Boolean Calculus ) Boole, Jevons, Peirce, Schroder (18xx) Axiomatic System: Huntington (1904) Algebraic system : set of elements B, two binary operations + and B has at least two elements (0 and 1) If the following axioms are true then it is a Boolean Algebra: A1. identity A2. complement A3. commutative A4. distributive ) ( ( ) ()
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Need to prove that a is the complement of NONO Property: Proof: Saying No Twice? A2 A3 Definition of complement: Q Definition and uniqueness of complement (T1) Are 0 and 1 complements?
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01 Complement: 01 Complement Property and Proof:
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01 Complement: 01 Complement Property and Proof: A1 A1 A3 Q
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Prove or Disprove At least one of the following is true: ist
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Syllogism to Algebra George Boole, 1847 George Boole 1815 –1864
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George Boole Early Days George Boole 1815-1864 Born in Lincoln, England an industrial town His father was a shoemaker with a passion for mathematics and science When George was 8 he surpassed his father’s knowledge in mathematics By age 14 he was fluent in Latin, German, French, Italian and English… and algebra… When his was 15 he had to go to work to support his family, he became a math teacher in the Wesleyan Methodist academy in Doncaster (40 miles…) Lost his job after two years…. Lost two more teaching jobs… When he was 20 he opened his own school in his hometown - Lincoln
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George Boole Early Career George Boole 1815-1864 Born in Lincoln, England an industrial town Why did he buy mathematics books? He did not have much money, and he discovered that math books took longer to master… He was mentored by the mathematician Duncan Gregory from Cambridge: 1813- 1844, Edinburgh, Scotland Never attended formal studies at a university? DG to GB: “you must be prepared to undergo a great deal of mental discipline , which is not agreeable to a man who is accustomed to think for himself” “A high degree here is due quite as much to diligent labor in certain appointed paths as to mathematical capacity
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George Boole 1815-1864 Born in Lincoln, England an industrial town He was mentored by the mathematician
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IST4_lec8 - IST 4 Information and Logic IST 4: Planned...

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