ECS 20 Study Guide - Summer 2018, Comprehensive Midterm Notes - Integer, Permutation, Sum Rule In Differentiation
12 Oct 2018
School
Department
Course
Professor
ECS 20
MIDTERM EXAM
STUDY GUIDE
Fall 2018
ECS 20 – Lecture 1-3
Office 3005 kemper
Set theory:
a. A set is a well-defined collection of objects
Notation: for set
For element
b. element is in the set
is not an element of
c. Specify set:
• By listing is elements, for example
• By showing those properties which characterizes the elements in the set
For example
Where is a set and is an element
• Vann diagram-pictorial representation (not rigorous)
Elements
A
d. Subset: consider sets and
Every
is a subset of
vs
By definition
Note, vs
Fact: if and then
Special sets/Subsets:
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Empty set for example
Note:
Universal set
Set equality
and
Union
Venn diagram:
ABDoes not need to intersect
C
A
A
Component
Intersection:
AB
Difference:
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find more resources at oneclass.com
Document Summary
Set theory: a set is a well-defined collection of objects. Notation: (cid:1827),(cid:1828),(cid:1829),(cid:1845), for set (cid:1845) (cid:1853),(cid:1854),(cid:1855) for element (cid:1845: (cid:1853)(cid:1488)(cid:1845) element (cid:1853) is in the set (cid:1845) (cid:1853)(cid:1489)(cid:1845) (cid:1853) is not an element of (cid:1845, specify (cid:1853) set, by listing is elements, for example(cid:1827)={(cid:883),(cid:885),5,(cid:889),(cid:891)} For example (cid:1827)={| is an odd integer and less than (cid:883)(cid:882)} Where (cid:1827) is a set and is an element: vann diagram-pictorial representation (not rigorous, by showing those properties which characterizes the elements in the set. Elements: subset: consider sets (cid:1827) and (cid:1828) (cid:1827) (cid:1828) every (cid:1488)(cid:1827),(cid:1488)(cid:1828) (cid:1827) is a subset of (cid:1828) Empty set for example (cid:1845)={| is a positive integer of (cid:2870)=(cid:885)}= (cid:1827) Independent law (cid:1827)(cid:1515)(cid:1827)=(cid:1827) and a(cid:1514)a=a: associative law (cid:4666)(cid:1827)(cid:1515)(cid:1828)(cid:4667)(cid:1515)(cid:1829)=(cid:1827)(cid:1515)(cid:4666)(cid:1828)(cid:1515)(cid:1829)(cid:4667, a set (cid:1845) is finite if (cid:1845) is empty or (cid:1845) contains exactly (cid:3021) elements (cid:3021) is a positive integer, = cardinality of (cid:1845)
