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Algorithum
A procedure for solving a problem.
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PERT Diagrams
- In box: Time takes to complete operation
- Out box: The total time added us thus far
- Critical Path: Colored backwards
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Permutations
- Set of objects, and any ordering of those objects.
- P(n,r) = n!/ (n-r)!
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Z
Set of integers= {...-2,-1,0,1,2....}
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N
- Set of Natural #'s = {0,1,2....}
- All non-negative numbers
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Z+
Set of positive integers = {1,2,3...}
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Q
Set of rational numbers = a/b b not equal to 0
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Statement
A sentence thats either true or false (has truth value)
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Negation
- ~ means opposite
- Statements with "some" change to "no"
- Statements with "all", "each" or "every" change to "some...not..."
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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
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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
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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
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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
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DeMorgans
- ~(pvq) <--> (~p) ^ (~q) *Switch signs with take negation
- ~(p^q) <--> (~p) v (~q)
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Tautology
Statement that's always true
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Proof by contridiction
Assume conclusion isn't true, and use this to arrive at a contradiction.
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