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