User talk:Ascii/ProofWiki Sampling Notes for Theorems/Set Theory


 * 1) a set is a subset of itself
 * 2) a singleton of an element of a set is a subset of that set
 * 3) the subset relation is transitive
 * 4) a set is equal to itself
 * 5) the empty set is a subset of all sets
 * 6) the empty set is unique
 * 7) the empty set is an element of any power set
 * 8) a set is an element of its own power set
 * 9) the power set of the empty set is the singleton of the empty set
 * 10) union is idempotent
 * 11) union is commutative
 * 12) union is associative
 * 13) the union of any set with the empty set is the set itself
 * 14) the union of two sets is a superset of each
 * 15) set union preserves subsets
 * 16) the union of two sets is the smallest set containing them both
 * 17) the union of two subsets is also a subset
 * 18) the union of a set with a superset is the superset
 * 19) union distributes over itself
 * 20) intersection is idempotent
 * 21) intersection is commutative
 * 22) intersection is associative
 * 23) the intersection of two sets is a subset of each
 * 24) the intersection of any set with the empty set is itself the empty set
 * 25) the intersection of a set with a superset is the set itself
 * 26) intersection distributes over itself
 * 27) the intersection of two sets is a subset of their union
 * 28) intersection distributes over union
 * 29) union distributes over intersection