# Set Theory: Subsets of P(N)

• NecroWinter
A is actually the power set of the natural numbers, which is the set of all possible subsets of the natural numbers. B is just the set containing the set {1}. For C, you have the right idea but the set should only contain 5 elements, not 6. So a correct answer could be {1,2,3,4,5}.In summary, set S can be any subset of the power set of natural numbers, including the set of all natural numbers or any set that contains the set {1}. If S must also have 5 elements, a possible answer could be {1,2,3,4,5}.

#### NecroWinter

Hi there, here's the question I am given, i will provide the answer that I think is correct, do you mind checking it and possibly pointing out where I am wrong if I am?

Give an example of a set S such that:
a) S is a subset P(N)
b) S belongs to P(N)
c) S belongs to P(N) and |S|=5

a) {1,2,3}
b) {{1}}
c) {1,2,3,4,5}

Hey NecroWinter and welcome to the forums.

Just to clarify what is the set P(N)? Is this just all the natural numbers or the power set of the entire set of natural numbers?

You have the answers for A and B switched.

## What is a subset?

A subset is a set that contains only elements that are also contained in another set. In other words, all the elements of a subset are also elements of the larger set.

## How do you determine if one set is a subset of another set?

To determine if one set is a subset of another set, you need to check if all the elements of the first set are also present in the second set. If this is true, then the first set is a subset of the second set.

## Can a set be a subset of itself?

Yes, a set can be a subset of itself. This is because all the elements of the set are also present in the set itself.

## What is the difference between a proper subset and an improper subset?

A proper subset is a subset that does not contain all the elements of the original set. An improper subset, on the other hand, contains all the elements of the original set and is equal to the original set. In other words, an improper subset is a subset that is not a proper subset.

## How many subsets can a set have?

A set can have an infinite number of subsets. This is because every element in the set can be either included or excluded in a subset, resulting in an exponential number of possible subsets.