# Discrete Math

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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.
 Author: lisrosey ID: 39696 Card Set: Discrete Math Updated: 2010-10-05 03:47:19 Tags: Discrete Math Folders: Description: Test 1 Show Answers: