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Confused on directions, List the elements in the subsets?

  1. Oct 11, 2006 #1
    Hello everyone. There arn't any problems like this in this section, so i'm kind of lost on what they want. It says...

    Let S = {a,b,c} and for each integer i = 0, 1, 2, 3 let [tex]S_i[/tex] be the set of all subsets of S that have i elements. List the elemnts in [tex]S_o,S_1,S_2,S_3[/tex]. Is {[tex]S_0,S_1,S_2,S_3[/tex]} a partion of P(S).
    P(S) stands for power sets.

    S_0 = {a_0,b_0,c_0}
    S_1 = {a_1,b_1,c_1}

    or what are they saying exactly?

    Isn't S_0 through 3 going to have the exact same elements just {a,b,c} all the time? I dont see how changing the subscript on S is changing the elements or the number of elements.

    I have no idea what they want, The only thing i saw in the book was the folllowing:
    THe number of subsets of a set.

    THe following theorem states the important fact that if a set has n elements, then its power set has 2^n elements.
    Suppose X is a set and z is an elemen tof X.

    If X = {x,y,z}, the following table shows the correspondence between subsets of X that do not contain z and subsets of X that contain Z.

    The table shows subset so X that do not contain z (X- {z} )

    Subsets of X that contain z
    NULL union {z} = {z}
    {x} union {z} = {x,z}
    {y} union {z} = {y,z}
    {x,y} union {z} = {x,y,z}

    But i don't see how this relates to my probem at all.

    Any help would be great
    Last edited: Oct 11, 2006
  2. jcsd
  3. Oct 11, 2006 #2


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    For example, for i = 2, S2 = {{a,b}, {b, c}, {a, c}}.

  4. Oct 11, 2006 #3
    Thanks for the responce but thats what confusees me, i know what a power set is, like if you find
    P({x,y}) = {NULL, {x},{y}, {x,y}}

    Are you taking the power set of S? in ur example?
    or how did u get {{a,b},{b,c},{a,c}} if that was a power set, isn't it suppose to be 2^n, so if i = 2, wouldn't u have 4 sets in there?

    When they say list the elments in S0 - S3, do they mean take the power set of S0 - S3? and if thats the case, how does the subscript affect whats in S = {a,b,c}?
    Last edited: Oct 11, 2006
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