Discrete Chapter 1

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Discrete Chapter 1
2012-09-11 11:36:37
Discrete Math

Section 1.1
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  1. Proposition
    Declarative sentence that is either true or false but not both
  2. Propositional variables
    • Variables that¬†represent propositions
    • p,q,r,s...
  3. Truth Value
    denoted by T or F
  4. Propositional Calculus
    the area of logic that deals with propositions (propositional logic)
  5. Compound Propositions
    formed from propositions by using logic operators
  6. Negation of p
    • it is not the case that p
    • not p
  7. Conjunction of p and q
    p and q
  8. Disjunction of p and q
    p or q
  9. Inclusive or
    one or the other or both
  10. Exclusive or
    one or the other but not both
  11. Conditional Statement
    • If p, then q.¬† Implication
    • p=hypothesis
    • q=conclusion
  12. Converse
    q -> p
  13. Contrapositive
    not q -> not p
  14. Inverse
    not p -> not q
  15. Equivalent
    two compound propositions that always have the same truth value
  16. bitwise OR, AND, XOR
    taken on bit strings by doing the operation on the corresponding bits
  17. Aristotle
    • greek orphan
    • Attended Pluto's Academy in Athes
    • tutor Alexander the Great
    • Start school called Lyceum
    • 3 types of work - popular, compliations, science
  18. Boole
    • England 1800's mathematicion
    • The Mathematical Analysis of Logic
    • Queens College - Ierland
    • The Laws of Thought - Boolean Algebra
  19. Tukey
    • Home School Mass
    • Brown for Chem, Princeton for Math & teach
    • AT&T Bell Lab
    • Coining of words bit and software