Question 1164590: list of all possible subset for each
1.{10,20}
2.{a,e,i,o,u}
3.{g,e,o,m}
4.{3,5,7}
5.(beta}
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
I'll do the first two problems to get you started.
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Problem 1
A set is a collection of things. Usually those things are numbers, but they could be anything really.
Let's say that A was some set and B was a subset of A. This would mean that everything inside B is also from A (but not necessarily the other way around).
An example of this would be comparing the set of vertibrates with the set of mammals. Any mammal is a vertibrate, but not vice versa. In terms of sets, if something is in the set "mammal" then it is also in the set "vertibrate". We can then say "the set of mammals is a subset of vertibrates".
With that out of the way, let's tackle the math problem.
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We have the set {10, 20}. It has two elements inside it.
One possible subset is the set itself. Any set is a subset of itself.
Another subset would be {10} which is a set with one item in it. This is called a singleton. The only other possible singleton subset would be {20}. Each singleton mentioned picked values from the original set.
Lastly, the empty set is a subset of the original set. The empty set is a subset of any set. We write the empty set as a pair of curly braces with nothing inside it.
There are four subsets and they are:
{10, 20} .... has 2 items
{10} ... has 1 item
{20} ... has 1 item
{ } ... has 0 items
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Problem 2
The original set {a,e,i,o,u} has five elements
{a,e,i,o,u} is one subset. Again, any set is a subset of itself.
{a,e,i,o} is a subset with 4 elements. So is {a,e,i,u} and {a,e,o,u} and so on. The four element subsets are basically the result of taking out one letter from the original set.
The list of four element subsets are
{a,e,i,o} ... removed letter 'u'
{a,e,i,u} ... removed letter 'o'
{a,e,o,u} ... removed letter 'i'
{a,i,o,u} ... removed letter 'e'
{e,i,o,u} ... removed letter 'a'
The list of three-element subsets are
{i,o,u} ... removed a,e
{e,o,u} ... removed a,i
{e,i,u} ... removed a,o
{e,i,o} ... removed a,u
{a,o,u} ... removed e,i
{a,i,u} ... removed e,o
{a,i,o} ... removed e,u
{a,e,u} ... removed i,o
{a,e,o} ... removed i,u
{a,e,i} ... removed o,u
This list is a bit more tricky, but look at the next section and it might help clear things up.
The list of two-element subsets are
{a,e}
{a,i}
{a,o}
{a,u}
{e,i}
{e,o}
{e,u}
{i,o}
{i,u}
{o,u}
The list of items here is basically the stuff we removed in the previous section.
The list of singletons are
{a}
{e}
{i}
{o}
{u}
And don't forget the empty set as well.
The full list of all subsets is given below
{a,e,i,o,u} .... 5 elements
{a,e,i,o} .... 4 elements
{a,e,i,u} .... 4 elements
{a,e,o,u} .... 4 elements
{a,i,o,u} .... 4 elements
{e,i,o,u} .... 4 elements
{i,o,u} ... 3 elements
{e,o,u} ... 3 elements
{e,i,u} ... 3 elements
{e,i,o} ... 3 elements
{a,o,u} ... 3 elements
{a,i,u} ... 3 elements
{a,i,o} ... 3 elements
{a,e,u} ... 3 elements
{a,e,o} ... 3 elements
{a,e,i} ... 3 elements
{a,e} ... 2 elements
{a,i} ... 2 elements
{a,o} ... 2 elements
{a,u} ... 2 elements
{e,i} ... 2 elements
{e,o} ... 2 elements
{e,u} ... 2 elements
{i,o} ... 2 elements
{i,u} ... 2 elements
{o,u} ... 2 elements
{a} ... 1 element
{e} ... 1 element
{i} ... 1 element
{o} ... 1 element
{u} ... 1 element
{ } ... empty set
There are 32 different subsets listed above.
For any given set, the order does not matter. Something like {a,e,i} is the same as {a,i,e}. Convention usually has things sorted in alphabetical or numeric order.
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Side note: if a set has n items inside it, then it has 2^n different subsets.
Another side note: The numbers in pascal's triangle are very helpful to determine the number of subsets. Note the numbers along the row 1,5,10,10,5,1 add up to 32. Those values refer to the counts of five-element subsets, four-element subsets, and so on.
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