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SETS Set-Theory - Coggle Diagram

- - - - A set which contains a definite number of elements is called a finite set.
        Example − S = { x | x ∈ N and 70 > x > 50 }
    - - A set which contains infinite number of elements is called an infinite set.
        Example − S = { x | x ∈ N and x > 10 }
  - - - If the cardinalities of two sets are same, they are called equivalent sets.
        Example − If A = { 1, 2, 6 } and B = { 16, 17, 22 }, they are equivalent as cardinality of A is equal to the cardinality of B. i.e. |A| = |B| = 3
    - - If two sets contain the same elements they are said to be equal.
        Example − If A = { 1, 2, 6 } and B = { 6, 1, 2 }, they are equal as every element of set A is an element of set B and every element of set B is an element of set A.
- - - - The union of two sets contains all the elements contained in either set (or both sets).
      - The union is notated A ⋃ B.
      - More formally, x ∊ A ⋃ B if x ∊ A or x ∊ B (or both)
  - - - The intersection of two sets contains only the elements that are in both sets.
      - The intersection is notated A ⋂ B.
      - More formally, x ∊ A ⋂ B if x ∊ A and x ∊ B
- - - - The relative complement or set difference of sets A and B, denoted A – B, is the set of all elements in A that are not in B.
      - In set-builder notation, A – B = {x ∈ U : x ∈ A and x ∉ B}= A ∩ B'.
      - The Venn diagram for the set difference of sets A and B is shown below where the shaded region represents A – B.
  - - - The complement of a set, denoted A', is the set of all elements in the given universal set U that are not in A.
      - In set- builder notation, A' = {x ∈ U : x ∉ A}.
      - The Venn diagram for the complement of set A is shown below where the shaded region represents A'.