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

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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 ab=ba

• Associative law: a+(b+c)=(a+b)+c

• Distributive law: a(b+c)= (ab)+(bc)

  • Commutative or

  • Associative

  • Distributive

-Mayank