When presenting sets, whether in written or mathematical form, it's important to follow conventions and notation to clearly convey the information about the set. Here are common ways to present sets:

  1. Roster Notation (Enumeration):- In roster notation, you list all the elements of the set within curly braces {}. Each element is separated by commas.Example: The set of even numbers less than 10 can be presented as {2, 4, 6, 8}.
  2. Set-Builder Notation (Description):- In set-builder notation, you describe the properties that define the elements of the set using a statement within curly braces {}. Example:- The set of all even positive integers can be presented as {x | x is a positive integer and x is even}.
  3. Interval Notation (for Continuous Sets):- Interval notation is often used for sets of real numbers or continuous ranges.Example: The set of real numbers between 0 and 1 (excluding 0 and 1) can be presented as (0, 1).
  4. Subset Notation:- To represent subsets or supersets of a set, you can use symbols like (subset) or (superset). Example: If A is a subset of B, you can write it as A ⊆ B.
  5. Complement Notation:- To denote the complement of a set, you can use the ' symbol or the "not" notation.Example: The complement of set A can be written as A' or "not A."
  6. Mathematical Operations (Union, Intersection, etc.):- Sets can also be presented through mathematical operations. Example:- The union of sets A and B can be written as A ∪ B.
  7. Venn Diagrams:- Visual representations like Venn diagrams can be used to illustrate the relationships between sets, especially when dealing with multiple sets and their intersections.
  8. Inequality or Range Notation (for Numerical Sets):- Inequality symbols (<, ≤, >, ≥) can be used to describe numerical sets. Example:- The set of integers greater than or equal to - 5 can be presented as {x | x ≥ -5}.
  9. Bold or Uppercase Letters (Conventional Notation):- In mathematics, uppercase letters like A, B, C are often used to represent sets. For example, A may represent the set of all even numbers.
  10. Cardinality Notation (| |):- The cardinality of a set (the number of elements) can be represented using vertical bars or absolute value symbols.Example: |A| represents the number of elements in set A.
  11. List Notation (Enumeration):-This method involves listing all the elements of the set within curly braces {}. Example:- The set of even numbers less than 10 can be represented as {2, 4, 6, 8}
  12. Mathematical Symbols:- Mathematical symbols can be used to represent sets and set operations.

Common symbols include:-

   ∅ or {} for the empty set,

   ∈ for "is an element of,

   ⊆ for "is a subset of,

   ∪ for union,

   ∩ for intersection

   ' for complement.

Example: A = {1, 2, 3}, B = {2, 3, 4}, then A ∪ B represents the union of sets A and B

  13. Set Diagrams (Tables or Matrices):-

  • For small sets, you can create tables or matrices to display elements and their properties.
  • Example:

| Set A | Set B |
| 1      |   2    |
| 2      |   3    |
| 3      |   4    |

  14. Textual Description:-

  • In some cases, sets can be described in plain text, especially when listing all elements explicitly is not practical.
  • Example: "The set of prime numbers less than 20."

When presenting sets, the choice of notation depends on the context and the specific information you want to convey. It's essential to use clear and precise notation to avoid any ambiguity and accurately represent the set's properties and elements.