-  This entire section consists of one type of problem.
    
        -  There is an (easy) two set variation
	
-  And a (harder) three set variation.
    
 
-  In either case, you must do a little arithmetic.  If you choose not to, don't do the problems.
    
-  Probably 20% of the next test.
    
-  Important : n(A ∪ B) = n(A) + n(B)  - n(A ∩ B)
    
-  n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)
    
-  At Least n  means n or more 
    
-   At Most n means n or less
    
-   and means in both
    
-   or  means in one or the other or both.
    
-  Problem 4 page 80
    
Fleet Foot Racing interviewed 150 long distance
runners to determine the type of races in which
they participated.  The following information was
determined
    102 participated in a marathon
     93 participated in a triathlon
     55 participated in a marathon and a triathlon.
How many participated in a marathon?
How many participated in a triathlon?
How many participated in both?
How many participated in none?
How many participated in exactly one?
How many participated in one or more?
    
-  Number 5 page 80
    
Thirty Tree US Cities were researched to determine
whether they had a professional sports team, a 
symphony, or a children's museum.  The following 
information was determined
    16 had a professional sports team
    17 had a symphony
    15 had a children's museum
    11 had a sports team and a symphony
     7 had a professional sports team and a 
       children's museum
     9 had a symphony and a children's museum
     5 had all three
How many had only a professional sports team
How many had a sports team and a symphony but not a children's museum
How many had a professional sports team or a symphony
How many had two or more activities
How many had at least one activity
How many had no activities
How many had exactly two activities
    
-  Number 10 page 81
    
In a survey of college students it was found that
     356 owned an iPod
     293 owned a laptop
     285 owned a gaming system
     193 owned an iPod and a laptop
     200 owned an iPod and a gaming system
     139 owned a laptop and a gaming system
     68 owned all three
     26 owned none of these
How many students were surveyed?
    
-  I made this one up
    
Find the error in the following:
In a survey of 100 people
   78 liked shrimp gumbo 
   54 liked shrimp  etouffee
   Therefore 132 liked either.