- #1
mr_coffee
- 1,629
- 1
Hello everyone I'm confused on how he got this...
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] copy.jpg[/PLAIN] 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 setand 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 separate brackets {{a,b,c}}
Any explanation 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.
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] copy.jpg[/PLAIN] 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 setand 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 separate brackets {{a,b,c}}
Any explanation 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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