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

    • 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 ab=ba

  • Associative law: a+(b+c)=(a+b)+c

  • Distributive law: a(b+c)= (ab)+(bc)

    • Commutative or

    • Associative

    • Distributive