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Math Help - Set Theory

  1. #1
    Member iPod's Avatar
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    Set Theory

    Hello,
    I have attached the question

    I'm not sure how to do a parts ii), iii), & iv)
    I don't know how to express the sets they give.
    Attached Thumbnails Attached Thumbnails Set Theory-set-q.png  
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  2. #2
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    Re: Set Theory

    Quote Originally Posted by iPod View Post
    Hello,
    I have attached the question
    I'm not sure how to do a parts ii), iii), & iv)
    I don't know how to express the sets they give.
    Here is a hint: A\cup B=\{25,30,35,40,23,33\}
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  3. #3
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    Re: Set Theory

    A is the set of all multiples of 5, B contains the two numbers 23 and 33, and C is the set of all prime numbers. (ii) Their union is {x: x is a multiple of 5 or x is prime or x = 33}. I did not need to include "x= 23" because 23 is prime. (iii) The complement is the set of all composite (non-prime) numbers that are NOT multiples of 5 and not equal to 33: {x: x is composite but not 33 or a multiple of 5}. (iv) should be very easy- what numbers in A or B are prime numbers?
    Last edited by HallsofIvy; July 22nd 2012 at 08:56 AM.
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  4. #4
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    Re: Set Theory

    Ah I see, all the numbers in the sets are limited between 20 up to and including 40. So,

     A\cup B \cup C = {25, 30, 35, 40, 23, 33, 29, 31, 37, 39}

    yeah?

    I think I can take it from here...
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  5. #5
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    Re: Set Theory

    Quote Originally Posted by iPod View Post
    Ah I see, all the numbers in the sets are limited between 20 up to and including 40. So,

     A\cup B \cup C = \{25, 30, 35, 40, 23, 33, 29, 31, 37, {\color{red}39}\}
    yeah?
    39 is not prime.
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  6. #6
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    Re: Set Theory

    Hello, iPod!

    I have to ask: did you write out the sets?


    Given: . \begin{Bmatrix} U &=& \{x\,|\,x\in I,\:20 < x \le 40\}  \\  A &=& \{x\,|\,x\text{ is a multiple of 5\}}  \\   B &=& \{23,\,33\} \\  C &=& \{x\,|\,x\text{ is prime}\} \end{Bmatrix}

    We have: . \begin{array}{ccc}U &=& \{21,22,23\,\hdots\,40\} \\ A &=& \{25,30,35,40\} \\ B &=& \{23,\,33\} \\ C &=& \{23,29,31,37\} \end{array}



    List the following sets:

    . . (i)\;B \cap C
    B \cap C \;=\;\{23,33\} \,\cap\,\{23,29,31,37\} \;=\;\{23\}


    (ii)\;A \cup B \cup C
    All three sets combined into one set . . .

    A \cup B \cup C \;=\;\{23,25,29,30,31,33,35,37,40\}



    (iii)\;\overline{A \cup B \cup C}
    This is the complement of the set in part (ii).

    \overline{A \cup B \cup C)} \;=\;\{21,22,24,26,27,28,32,34,36,38,39\}



    (iv)\;(A \cup B) \cap C
    (A \cup B) \cap C \;=\;\bigg(\{25,30,35,40\} \,\cup \,\{23,33\}\bigg) \,\cap \,\{23,29,31,37\}

    . . . . . . . . . . =\;\{23,25,30,33,35,40\} \cap \{23,29,31,37\}

    . . . . . . . . . . =\;\{23\}




    Shade the following regions.

    . . (i)\;(A \cup B) \cap C
    Code:
          * - - - - - - - - - - - - - - - - - - - * 
          |                                       |
          |           o o o       o o o           |
          |       o           o           o       | 
          |     o     A     o   o     B     o     | 
          |    o           o     o           o    | 
          |                                       |
          |   o           o       o           o   |
          |   o           o o o o o           o   |
          |   o         o o:::::::o o         o   |
          |           o:::::::::::::::o           | 
          |    o     o:::::o:::::o:::::o     o    |
          |     o    :::::::o:::o:::::::    o     | 
          |       o o:::::::::o:::::::::o o       | 
          |         o:o:o:o       o:o:o:o         | 
          |         o                   o         | 
          |                                       | 
          |          o                 o          | 
          |           o       C       o           | 
          |             o           o             | 
          |                 o o o                 | 
          |                                       | 
          * - - - - - - - - - - - - - - - - - - - *


    (ii)\;A \cup (B \cap C)
    Code:
          * - - - - - - - - - - - - - - - - - - - * 
          |                                       |
          |          .o o o.      o o o           |
          |       o:::::::::::o           o       | 
          |     o:::::A:::::o:::o     B     o     | 
          |    o:::::::::::o:::::o           o    | 
          |   .::::::::::::::::::.                |
          |   o:::::::::::o:::::::o           o   |
          |   o:::::::::::o:o:o:o:o           o   |
          |   o:::::::::o:o:::::::o o         o   |
          |   ::::::::o:::::::::::::::o           | 
          |    o:::::o:::::o:::::o:::::o     o    |
          |     o:::::::::::o:::o:::::::.   o     | 
          |       o:o:::::::::o:::::::::o o       | 
          |         o o o o       o:o:o:o         | 
          |         o                '''o         | 
          |                                       | 
          |          o-                o          | 
          |           o       C       o           | 
          |             o           o             | 
          |                 o o o                 | 
          |                                       | 
          * - - - - - - - - - - - - - - - - - - - *
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