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

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Watch Video Lecture on YouTube: Sets: Union, Intersection, Disjoint, Subset, Superset, Equal, Null, Empty, Universal

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

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Set Notations

By enumeration or description

  • S={2,3,4)

  • 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 2^n 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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