Sets and Set Operations .edu

CSCE 222

Discrete Structures for Computing

Sets and Set Operations

Dr. Philip C. Ritchey

Set Notation

? Set: an unordered collection of objects (��members��, ��elements��)

??��?

? ��? is a member of ?��, ��? is an element of ?��

????

? ��? is not a member of ?��, ��? is not an element of ?��

? Roster method

? S= 1,2,3,4

? Set Builder

? ? = ? �O ? ?? ? ???????? ??????? ???? ???? 5

? ? = ? �O ? �� ?+ �� ? < 5

Exercise

? Jumping Jacks!

? Kidding��

? List the members of the set:

? ? �O ? ?? ??? ?????? ?? ?? ??????? ??? ? < 100

? 0,1,4,9,16,25,36,49,64,81

? ? �O ?2 = 2

? ? 2, 2

? Use set builder notation to describe the set:

? 0,3,6,9,12

? 3? �O ? ?? ?? ??????? ??? 0 �� ? �� 4

? ?3, ?2, ?1,0,1,2,3

? ? �O ? ?? ?? ??????? ??? ? �� 3

Common Sets

? ? = �� , ?2, ?1,0,1,2, �� , the set of integers

? ?+ , the positive integers

? ?? , the negative integers

? ? = [0, ]1,2,3, �� , the set of natural numbers

?

? ? = �O ?, ? �� ?, ? �� 0 , the set of rational numbers

?

? ?, the set of real numbers

? ?+ , the set of positive reals

? ?? , the set of negative reals

? ?, the set of complex numbers

? ?: the universal set (set of discourse)

? ?: the empty set,

? ? is a non-empty singleton set

Interval Notation

? Shortcuts for sets containing numbers

? [ , ] mean inclusive. Closed interval.

? ( , ) mean exclusive. Open interval.

?, ? = ? �O ? �� ? �� ?

?, ? = ? �O ? < ? < ?

?, ? = ? �O ? �� ? < ?

?, ? = ? �O ? < ? �� ?

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download