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Thread: PSAT Review

  1. #1

    PSAT Review

    Set A has K elements and set B has m elements, where m>k . Sets A and B have 2 elements in common. How many elements in the union of the two sets are members of only one of the sets? a) m+k-4b) m+k-2c)m-kd) m-k+2e) m-k+4

    And can someone give me a thorough explanation? I have no idea how to do this...Thank you so much

  2. #2
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    Quote Originally Posted by sathelp View Post
    Set A has K elements and set B has m elements, where m>k . Sets A and B have 2 elements in common. How many elements in the union of the two sets are members of only one of the sets? a) m+k-4b) m+k-2c)m-kd) m-k+2e) m-k+4

    And can someone give me a thorough explanation? I have no idea how to do this...Thank you so much
    The union is the set of all elements belonging to both. So m+k would be correct if the sets were disjoint​, i.e., having no elements in common. They have elements in common, so m+k double counts some elements. What adjustment should you make then?

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    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by sathelp View Post

    I have no idea how to do this
    One way is to make up some small sets to model the given information and then play with them. Analyze to see whether you find a multiple-choice expression that consistently gives your manual results, using the values that you assigned to m and k.

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    Another way of looking at this: A has k elements and 2 of them are also in B. How many of the elements in A are NOT in B? B has n elements and 2 of them are also in A. How many of them are NOT in A?

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    Hello, sathelp!

    Evidently you have never heard of a Venn diagram.


    Set A has k elements and set B has m elements, where m > k.
    Sets A and B have 2 elements in common.

    How many elements in the union of the two sets are members of only one of the sets?

    . . [tex]a)\;m+k-4 \qquad b)\;m+k-2 \qquad c)\;m-k \qquad d)\;m-k+2\qquad e)\;m-k+4[/tex]

    Set [tex]A[/tex] has [tex]k[/tex] elements.
    Code:
                      o o o
                  o           o
                o       A       o
               o                 o
     
              o                   o
              o                   o
              o     k elements    o
    
               o                 o
                o               o
                  o           o
                      o o o

    Set [tex]B[/tex] has [tex]m[/tex] elements.
    Code:
                                  o o o
                              o           o
                            o       B       o
                           o                 o
    
                          o                   o
                          o                   o
                          o     m elements    o
    
                           o                 o
                            o               o
                              o           o
                                  o o o

    Sets [tex]A[/tex] and [tex]B[/tex] have 2 elements in column.
    The diagram looks like this:
    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   m - 2   o   2   o   k - 2   o
              o           o       o           o
    
               o           o     o           o
                o           o   o           o
                  o           o           o
                      o o o       o o o
    Got it?

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