Introduction of Set theory

a set is a collection of objects (called members or elements) that is regarded as being a single object. To indicate that an object x is a member of a set A one writes x ∊ A, while x ∉ A indicates that x is not a member of A.

  • A ∪ B—read “A union B” or “the union of A and B
  • A ∩ B—read “A intersection B” or “the intersection of A and B
  • U is called the universal set
  • A′ or U − A is called as complement of A
  • Cartesian product: Let A and B be two sets. Cartesian product of A and B is denoted by A × B, is the set of all ordered pairs (a,b), where a belong to A and B belong to B.

A × B = {(a, b) | a ∈ A ∧ b ∈ B}

  • if every element in A is also in B and every element in B is in A; symbolically, x ∊ A implies x ∊ B and vice versa.

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