Hello everyone. There arn't any problems like this in this section, so i'm kind of lost on what they want. It says...(adsbygoogle = window.adsbygoogle || []).push({});

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} )

Null

{x}

{y}

{x,y}

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

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# Homework Help: Confused on directions, List the elements in the subsets?

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