Set Basic Terminologies

• An element is an item within a given set which can be another set. It is denoted by ∈ (element) or ∉ (not an element).
• Element

  
• An empty/null set it is a special set that has NO elements. It is denoted by { } or Ø.
• Empty/Null Set

  
• A cardinality is the number of elements in each set. It is denoted by |S|.
• Cardinality

  
• An equality sets are two sets that are equal if and only if they contain exactly the same elements. Order is NOT important. It is denoted by =.
• Equality Set

  
• An equivalent sets are two sets that are equivalent if they contain the same number of elements. It is denoted by ~.
• Equivalent Set

  
• A subset is a set where every element of the subset is also an element of another set, or it is a sub collection of a given set. It is denoted by ⊆.
• If all the elements of a set A are also elements of a set B, then we say that A is a subset of B: A ⊆ B, or B is a subset of A: B ⊆ A
• Subset

  
• A proper subset is a subset where the set is not equal to the set, or sub-collection of a given set but not all elements of the larger set. It is denoted by ⊂.
• A set can be considered a proper subset, if there is at least one element in set B, which is not present in set A, and we write it as: A ⊂ B
• Proper Subset

  
• A power set is the set of all subsets of the set S. It is denoted by P(S).
• An empty set is a subset of any set, we write it as: Ø ⊆ S
• If a set A has n elements, It has 2n subsets; and 2n – 1 for the proper subsets.
• Power Set