Proper Subset


Empty Set

  • A Set that contains element
  • Represented with or
  • , but and , where contains 1 element

Not a Null Set

Theorem 6.2.4


  • A Set with exactly one element

Mutually Disjoin Subset

  • Also known as Pairwise Disjoint or Non-overlapping*
  • Refer to Partition, the elements inside partition are Mutually Disjoin
  • is called Union of Mutually Disjoint Subsets
  • The collection of sets is said to be a partition of

Disjoin Set

  • Given 2 Set, both don’t have any elements in common


  • is one of the mutually disjoin subset, also known as component of the partition
  • is the partition
  • So basically each isn’t empty, and its elements are not in other mutually disjoin subset

Theorem 8.3.1

Power Set

  • The power set of Set is all the possible Subset of
  • Given ,

Theorem 6.3.1

  • The cardinality of Superset of finite set is