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mr_coffee
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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 don't 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
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 don't 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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