
Algorithum
A procedure for solving a problem.

PERT Diagrams
 In box: Time takes to complete operation
 Out box: The total time added us thus far
 Critical Path: Colored backwards

Permutations
 Set of objects, and any ordering of those objects.
 P(n,r) = n!/ (nr)!

Z
Set of integers= {...2,1,0,1,2....}

N
 Set of Natural #'s = {0,1,2....}
 All nonnegative numbers

Z^{+}
Set of positive integers = {1,2,3...}


Q
Set of rational numbers = a/b b not equal to 0

Statement
A sentence thats either true or false (has truth value)

Negation
 ~ means opposite
 Statements with "some" change to "no"
 Statements with "all", "each" or "every" change to "some...not..."

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

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

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

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

DeMorgans
 ~(pvq) <> (~p) ^ (~q) *Switch signs with take negation
 ~(p^q) <> (~p) v (~q)

Tautology
Statement that's always true

Proof by contridiction
Assume conclusion isn't true, and use this to arrive at a contradiction.

