Discrete Math

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Author:
lisrosey
ID:
39696
Filename:
Discrete Math
Updated:
2010-10-04 23:47:19
Tags:
Discrete Math
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Description:
Test 1
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  1. Algorithum
    A procedure for solving a problem.
  2. PERT Diagrams
    • In box: Time takes to complete operation
    • Out box: The total time added us thus far
    • Critical Path: Colored backwards
  3. Permutations
    • Set of objects, and any ordering of those objects.
    • P(n,r) = n!/ (n-r)!
  4. Z
    Set of integers= {...-2,-1,0,1,2....}
  5. N
    • Set of Natural #'s = {0,1,2....}
    • All non-negative numbers
  6. Z+
    Set of positive integers = {1,2,3...}
  7. R
    All real numbers
  8. Q
    Set of rational numbers = a/b b not equal to 0
  9. Statement
    A sentence thats either true or false (has truth value)
  10. Negation
    • ~ means opposite
    • Statements with "some" change to "no"
    • Statements with "all", "each" or "every" change to "some...not..."
  11. Conjunction
    • Formed by joining the statements with the word "and"
    • p^q
    • p q p^q
    • T T T
    • T F F
    • F T F
    • F F F
    • *Both need to be True to be True
  12. Disjuction
    • Formed by joining the statements with the word "or"
    • Inclusive "or": One or other, or both
    • pvq
    • p q pvq
    • T T T
    • T F T
    • F T T
    • F F F
    • * Need to have at least one T to be True
  13. Conditional
    • "If....then..." statement
    • p->q
    • "If p then q": p implies q
    • p q p->q
    • T T T
    • T F F
    • F T T
    • F F T
    • *q must be true or p and q need to be the same
  14. Biconditional
    • If and only if statements
    • p<->q:
    • p q p->q q->p p<->q
    • T T T T T
    • T F F T F
    • F T T F F
    • F F T T T
    • *Have to match both ways
  15. DeMorgans
    • ~(pvq) <--> (~p) ^ (~q) *Switch signs with take negation
    • ~(p^q) <--> (~p) v (~q)
  16. Tautology
    Statement that's always true
  17. Proof by contridiction
    Assume conclusion isn't true, and use this to arrive at a contradiction.

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