Sets YouTube Lecture Handouts: Set Notations, Relationship of Sets, Operations, Laws of Sets

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Sets: Union, Intersection, Disjoint, Subset, Superset, Equal, Null, Empty, Universal

Set Notations

By enumeration or description

I = {x|x is positive integer}

I is set of all numbers x, such that x is positive integer

Set is finite number of elements , not ordered

2

Relationship of Sets

  • Equal
  • Disjoint
  • Subset/Superset
  • Null or empty set (different from {0} )
  • Universal set
  • 2 sets – some element in common but some are peculiar (so neither equal, nor disjoint, nor subset)
    • If set as n elements – then total subsets are formed

Operations

  • Union
  • Intersection
  • Complement
  • Universal

Laws of Set Operations

  • Commutative Law a + b = b + a or a b = b a
  • Associative law: a + (b + c) = (a + b) + c
  • Distributive law: a (b + c) = (a b) + (b c)
    • Commutative or
    • Associative
    • Distributive

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