SETS AND THEIR REPRESENTATION

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  • A set is well defined collection of objects.
  • sets can be represented in two ways:
  1. Roaster or tabular form, e.g. set of vowels is represented as { a, e, i, o, u } 
  2. Set-builder form, e.g. V = { x : x is a vowel in English alphabet }, V denote the given set. It is read as " the set of all x such that x is a vowel in English alphabet ".
  • The theory of sets was developed by German mathematician Georg Cantor ( 1845-1918 ). He first encountered sets while working on trigonometric series.
  • A set does not change if one or more elements of the set are repeated, e.g. A = { 1, 2, 3 } and B = { 2, 2, 1, 3, 3 } are equal.
  • Venn diagrams: Sets can be represented by means of diagrams known as Venn diagrams. These consist of rectangles and closed curves usually circles. Venn diagrams are named after English logician John Venn ( 1834-1883 ).

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