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Definitions edit

Subset edit



Subset means for all x, if x is in A then x is also in B.

Proper Subset edit



Union edit





Intersection edit





Empty Set edit



Minus edit



Powerset edit



Ordered Pair edit



Cartesian Product edit





Relation edit

A set of ordered pairs

Domain edit


Range edit


Field edit


Equivalence Relations edit

  • 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 edit

  • Transitive and,
  • Irreflexive: for all a, <a, a> not in R

Trichotomy edit

Exactly one of the following holds

  • x < y
  • x = y
  • y < x

Proof Strategies edit

If, then edit

Prove if x then y

Suppose x
so, y

If and only If edit

Prove x iff y

suppose x
so, y
suppose y
so, x

Equality edit

Prove x = y

show x subset y
show y subset x

Non-Equality edit

Prove x != y

x = {has p}
y = {has p}
a in x, but a not in y