Results 1 to 2 of 2

Math Help - Set Counting Problem

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    16

    Question Set Counting Problem

    The problem is:

    In carrying out a survey of the efficiency of the lights, brakes and steering of motor vehicles, 100 vehicles were found defective as follows:

    35 defective lights
    40 had defective brakes
    41 had defective steering
    8 had defective lights and brakes
    7 had defective lights and steering
    6 had defective brakes and steering

    a) how many had defective lights, brakes and steering?
    b) how many vehicles had defective lights only?

    Now I know the answers are 5 and 25 respectively but I cannot form the correct equation to arrive at them.

    I think the equation has to be in the form of

    x(A u B u C)= x(A) + x(B) + x(C) - x(A n B) - x(A n C) - x(B n C) + (A n B n C)

    I would appeciate help with the formulae.

    Many thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,713
    Thanks
    633
    Hello, barc0de!

    In carrying out a survey of the efficiency of the lights, brakes and steering of motor vehicles,
    100 vehicles were found defective as follows:

    35 defective lights
    40 had defective brakes
    41 had defective steering
    8 had defective lights and brakes
    7 had defective lights and steering
    6 had defective brakes and steering

    a) How many had defective lights, brakes and steering?

    b) How many vehicles had defective lights only?

    Now I know the answers are 5 and 25 respectively,
    but I cannot form the correct equation to arrive at them.

    I think the equation has to be in the form of:
    . . x(A\cup B \cup C) \:= \:x(A) + x(B) + x(C) - x(A\cap B) - x(A \cap C) -\; x(B \cap C) + (A \cap B \cap C)
    . . Right!

    We are given:. . \begin{array}{ccc}<br />
x(L\cup B\cup S) &=& 100 \\ x(L) &=& 35 \\ x(B) &=&40 \\x(S) &=&41 \\<br />
x(L\cap B) &=&8 \\ x(L\cap S) &=& 7 \\ x(B \cap S) &=& 6<br />
\end{array}\quad\hdots\quad\text{ and we want }x(L \cap B \cap S)

    Our equation is:

    . . x(L \cup B \cup S) \;=\;x(L) + x(B) + x(S) - x(L \cap B) -\; x(L \cup S) - x(B \cap S) + x(L \cap B \cap S)

    . . . . . 100 \qquad\;=\quad 35 \;+\; 40 \;\;+\;\; 41 \quad\;-\quad\;\; 8 \quad\;\; -\quad\;\;\; 7 \quad\;\;-\quad\;\;\; 6 \quad\;\;+ x(L \cap B \cap S)


    (a) And we have: . 100\:=\:95 + x(L \cap B \cap S) \quad\Rightarrow\quad \boxed{x(L\cap B\cap S) \:=\:5}



    The best way solve part (b) is with a Venn diagram.

    Or we can invent a formula for this situation . . .

    We want: . x(L \cap B' \cap S')


    And: . x(L \cap B' \cap S') \;=\;x(L) - x(L \cap B) - x(L \cap S) + x(L \cap B \cap S)

    . . . . . . . . . . . . . . = \;\;\; 35 \quad\;-\;\quad 8 \quad\;-\qquad 7 \quad\; +\qquad\;\; 5\quad=\quad\boxed{25}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Another counting problem
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 19th 2011, 07:11 AM
  2. Counting problem
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: July 11th 2010, 06:47 AM
  3. counting problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 16th 2010, 06:43 AM
  4. Replies: 3
    Last Post: April 13th 2009, 05:42 PM
  5. Counting problem
    Posted in the Statistics Forum
    Replies: 4
    Last Post: August 13th 2007, 12:01 PM

Search Tags


/mathhelpforum @mathhelpforum