Hello everyone i'm confused on how he got this...(adsbygoogle = window.adsbygoogle || []).push({});

the question says:

Let S = {a,b,c} and for each integer i = 0, 1, 2, 3, let S_i be the set of all subests of S that have i elements. List the elements in S_o,S_1,S_2,S_3. Is {S_0,S_1,S_2,S_3} a partion of P(S)?

Here is the answer:

http://suprfile.com/src/1/3rmvhz6/Untitled-1[/URL] [Broken] copy.jpg[/PLAIN] [Broken]

I know if i = 0,

S_0 = {NULL}

Is it NULL becuase 0 stands for somthing to be empty?

then i'm really lost on S_1 through S_3

Why did they break S = {a,b,c} into S_1 = {{a},{b},{c}}

If i stands for the # of elements then why would S_1 have 3 elements? not 1 element?

S_0, i = 0, means S_0 has 0 elemnets which makes sense to me becuase NULL means no elements or empty set

and for S_2 i'm confused on where they are getting those, its not hte power series becuase they didn't include {a,b,c} nor did they inlude the NULL set.

Then S_3, i'm confused why they just put it all into a seperate brackets {{a,b,c}}

Any explaination would be great!

I looked up the deinfition of a subset and it really doesn't help me make senes of this, it says a subset is the following:

If A and B are sets, then A is called a subset of B, if and only if, every element of A is also an lelemnt of B.

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# Can someone explain subsets to me? Not sure how he got this, answers posted!

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