Q1: math

• Sets

  • Well-defined: It must be clear whether an object is an element of a set or not
  • Unordered: The order of elements in a set does not matter
  • No repetitions: Each element appears only once in a set
• Ways to Represent Sets

  • Roster notation: Listing all elements within curly braces
  • Set-builder notation: Describing the elements using a rule
  • Venn diagrams: Using diagrams to visually represent sets and their relationships
• Types of Sets

  • Empty set (∅ or {}): A set containing no elements
  • Finite set: A set with a limited number of elements
  • Infinite set: A set with an unlimited number of elements
  • Subset: A set whose elements are all contained within another set
  • Proper subset: A subset that is not equal to the original set
  • Power set: The set of all subsets of a given set
• Set Operations

  • Union (∪): The set containing all elements from both sets
  • Intersection (∩): The set containing elements common to both sets
  • Difference ( - ): The set containing elements in the first set but not in the second
  • Complement ( ' ): The set containing all elements not in the original set (relative to a universal set)