How many total subsets can be made of the set: {A,L,V,I,N}?

[nckoliss]

i am on our UIL team for math and i came across a question in our competition that not evan my math teacher knows how to do. can anyone help me. the question geos like this-

How many total subsets can be made of the set: {A,L,V,I,N}.

the competition is over and i won't get to do it again till next year, but i still would like to know how to do. please help
here is another one i had that i need help on too.

the number of elements in the power set of {B,E,L,T,O,N}.

all i realy want to know is how to do it and can you tell me what it's called.

 

[royhaas]

Re: help please i don't evan know what it's called

The power set is the collection of all subsets of a given set, including the set itself and the null set. A set with \(\displaystyle N\) elements gives a power set of \(\displaystyle 2^N\) members.

 

[nckoliss]

i still don't understand. i know nothing about this by the way

 

[galactus]

It means you can make \(\displaystyle 2^{n}\) subsets from a set with n elements. Yours has 5 elements, so \(\displaystyle 2^{5}=32\) subsets can be made.

 

[nckoliss]

so if i understand this right, each letter is an element, and that number becomes an exponent over 2, and that is my answer?

 

[A_G]

In case you are wondering why this is so:
A set with n number of elements can have numerous subsets (a subset is all possible combination you can think of made with the elements of the given set):
1. A set with no element (also called the NULL set) {}
2. Sets with 1 element like {A}, {L}, {V} and so on in your case
3. Sets with 2 elements like {A,L}, {A,V}, {A,I}, {L,V} and so on in your case
4. Sets with 3 elements like {A,L,V}, {L,V,N}, {A,I,N} and so on in your case
.
.
.
.
n. A single set with all the elements of the given set {A,L,V,I,N}

So the total number of subsets = [supqr0ggo6]n[/supqr0ggo6]C[subqr0ggo6]0[/subqr0ggo6]+[supqr0ggo6]n[/supqr0ggo6]C[subqr0ggo6]1[/subqr0ggo6]+[supqr0ggo6]n[/supqr0ggo6]C[subqr0ggo6]2[/subqr0ggo6]+......+[supqr0ggo6]n[/supqr0ggo6]C[subqr0ggo6]n[/subqr0ggo6]
As per the Binomial Theorem (I guess that's what it is called) the above sum culminates to 2[supqr0ggo6]n[/supqr0ggo6]

 

[nckoliss]

ok. i got most of it now