Sets and Set Operations

Objectives:
  • Determine if a set is well defined.
  • Write all the subsets of a given set and label the subsets as proper or improper.
  • Given a universal set and some subsets, find a complement, intersection or union.
  • Draw a Venn diagram to illustrate two sets.
  • Use the cardinal number formula.



Vocabulary:
  • roster notation
  • set-builder notation
  • well defined set
  • cardinal number
  • empty set
  • subset
  • proper/improper subset
  • intersection of sets
  • union of sets
  • mutually exclusive
  • complement of a set
Term Symbol Read as
union

intersection

complement

subset



Cardinal Number Formula for Union of Sets:


Cardinal Number Formula for Complement of a Set:


Symbol Term

empty set

in

not in

number


Possible Classroom Examples:
  • the set of all pink automobiles
  • the set of all good bands
  • the set of odd numbers
  • the set of small numbers
If n of things in A union B is 40, find n of things in A intersection B and draw a Venn diagram illustrating the composition of U.

I am a member of a private gym.

I am a vegetarian.
The results were tabulated as follows:  374 checked the gym box, 92 checked the vegetarian box, and 332 were blank (no boxes checked).
a.  Draw a Venn diagram illustrating the results of the survey.
b. 
What percent of these men were both members of a private gym and vegetarians?

a.  clubs or twos
b. 
face cards or diamonds
c. 
threes or sixes
d. 
threes and sixes
Picture of a Standard Deck of Playing Cards
Hearts – Red

Diamonds – Red
Clubs – Black

Spades – Black



© 2007 Elizabeth E. K. Jones and the ASU Department of Mathematics and Statistics - All rights reserved.