Principles of Math Exam

  1.  Determine whether the following sets are defined or not well defined
  1.    The set of important courses at RCSJ
  2.    The set of two time Grammy award winners.
  1. Express each set in Roster Form  
    1.  
      1.     The set of Months that do not end in “r”
      2.     E = {x | x ∈ N and 22 < x ≤ 38 }
  1. Express each set in Set-Builder Notation 
  1. C = {21, 28, 35, 42, 49, 56}
  2. A is the set of months that have >30 days.
  1. Refer to Figure T1-4 on the “Test No 1 Information and Fact-Concept Sheet”. Use the graph to represent the set of years in which the cost of a Super Bowl commercial was less than or equal to $2.75 M.
  1. Answer true or false.  If false give the reason.
    1. {baseball, football, soccer} ⊂  {football, baseball, soccer}
    2. {  } ∈ {baseball, football, soccer}
  1. Determine whether A=B, A⊆B, A⊂B, B⊆A, B⊂A or none of these apply.   There may be more that one answer.

                  A is the set of sedans produced by Toyota

                  B is the set of all vehicles produced by Toyota

  1. If X⊆Z and Z⊆X, what other relationships exist between X and Z?
  1. Doogie is ordering a pizza at a restaurant. He can purchase a pizza consisting of just crust/sauce/cheese or he can add any of the following items: peppers, olives, onions, mushrooms, sausage, meatballs. How many different variations of a pizza are possible.
  1. For the sets U, A and B, construct a Venn diagram and place the elements in the proper regions.  

             U = {1st Base, 2nd Base, 3rd Base, Shortstop, catcher, pitcher, left field,

                     right field, center field}

             A =  {right field, center field, left field}

             B =  {1st Base, 2nd Base, 3rd Base}

  1. Refer to Figure T1-10 on the “Test No 1 Information and Fact-Concept Sheet”. That table shows the annual sales revenue and net income, in millions of dollars, for a major us manufacturing company for the years 2009-2013.  Let those years represent the Universal Set.

                  Let A = the set of years in which sales revenue was at least $1.5 Billion

                  Let B = the set of years in which net income was greater than $500 Million.

           Construct a Venn diagram illustrating the sets.

  1. The results of a survey of customers at a hair salon showed that 26 got their hair cut, 38 got a manicure and 14 got a manicure and their hair cut. How many got either a manicure or their hair cut?
  1. Refer to Figure T1-13 on the “Test No 1 Information and Fact-Concept Sheet”.

           Use the Venn Diagram on the figure to list the sets in roster form

  1.  A ∩ (C ∪ B )
  2. C

 13.      Refer to Figure T1-14 on the “Test No 1 Information and Fact-Concept Sheet”.

Write a description of the shaded area.  Use union, intersection and compliment as necessary. 

14.      Use a Venn Diagram or DeMorgan’s Laws to determine whether the following

           statements are equal  —  B’  ∪A’    and     (A ∪ B)

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