Set Theory/Review

Need help creating math symbols? Definitions Subset Subset means for all x, if x is in A then x is also in B. Proper Subset Union Intersection Empty Set Minus Powerset Ordered Pair Cartesian Product or Relation A set of ordered pairs Domain Range Field Equivalence Relations Reflexive: A binary relation R on A is reflexive iff for all a in A, <a, a> in R Symmetric: A rel R is symmetric iff for all a, b if <a, b> in R then <b, a> R Transitive: A relation R is transitive iff for all a, b, and c if <a, b> in R and <b, c> in R then <a, c> in R Partial Ordering Transitive and, Irreflexive: for all a, <a, a> not in R Trichotomy Exactly one of the following holds x < y x = y y < x Proof Strategies If, then Prove if x then y Suppose x ... ... so, y If and only If Prove x iff y suppose x ... ... so, y suppose y ... ... so, x Equality Prove x = y show x subset y and show y subset x Non-Equality Prove x != y x = {has p} y = {has p} a in x, but a not in y