Lec06_Set_Theory

# Lec06_Set_Theory - [Lecture 06[Set Theory Discrete...

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: [Lecture 06][Set Theory] Discrete Structures 1 [Lecture 06][Set Theory] TDS1191 Discrete Structures Lecture 06 Set Theory Multimedia University Trimester 2, Session 2011/2012 [Lecture 06][Set Theory] Discrete Structures 2 [Introduction] Set, Elements Equal, Cardinality Subset, Power Set [Set Operations] Union, Intersection, Difference, Complement Set Identities [Lecture 06][Set Theory] Discrete Structures 3 Basic Notations/Properties of Sets A set is simply an unordered collection of objects/elements/members. Sets are usually denoted as follows S = {a, b, c} T = {x | P(x)} where P is a predicate x ∈ S (“x is an element of S”) is the proposition that object x is an element or a member of the set S. Examples: 3 ∈ N if N = {0, 1, 2, 3, 4, …} a ∈ T if T = {x | x is a letter of the English alphabets} x ∉ S : ≡ ¬ (x ∈ S) “x is not in S” Exercise: What is the truth value of each of the following propositions? i.{4} ∈ {x | x is an odd number} T/F ii.e ∈ {x | x is a vowel} T/F iii.cat ∈ {x | x is an animal} T/F iv.Peter ∈ {x | x is a good boy} T/F An example of a predicate: P(x) : “x is a course offered by FIT” Exercise: What is the truth value of each of the following propositions? i.{4} ∈ {x | x is an odd number} T/ F ii.e ∈ {x | x is a vowel} T /F iii.cat ∈ {x | x is an animal} T /F iv.Peter ∈ {x | x is a good boy} T/F [Lecture 06][Set Theory] Discrete Structures 4 Basic Notations/Properties of Sets – Common Sets to Remember N = {0, 1, 2, 3, 4, 5, …} Set of natural numbers Z = {…, - 2, - 1, 0, 1, 2, …} Set of integers Z + = {1, 2, 3, …} Set of positive integers Q = { p / q | p ∈ Z, q ∈ Z, q ≠0} Set of rational numbers R = {All real numbers} Set of real numbers Examples of real numbers:-12.66547, 100000000.02, 244.0, Another name for rational number is fraction 2 Another name for natural number is counting number [Lecture 06][Set Theory] Discrete Structures 5 Basic Notations/Properties of Sets II S = T if and only if ( 2200 x : x ∈ S ↔ x ∈ T) Exercise: Given M 1 = { x | x is an integer where x >0 and x <5 } M 2 = { x | x is a positive integer whose square is >0 and <25} Decide whether M 1 = M 2. Hence, two sets are equal iff they have the same members. It does not matter how the set is defined or denoted! Set equality This is read as: For all x , x is an element of set S if and only if x is an element of set T. [Lecture 06][Set Theory] Discrete Structures 6 Basic Notations/Properties of Sets III Exercise: |{cat,rabbit,parrot}| = ____ |{a,b}| = ___ |{{1,2,3},{4,5}}| = ____ |{ x | x is even and x < 11}| = ___ Can you think of some examples of infinite sets?...
View Full Document

{[ snackBarMessage ]}

### Page1 / 25

Lec06_Set_Theory - [Lecture 06[Set Theory Discrete...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online