Subsets of sets

Original post by loryn95

Hi,

If I have a the following sets, what will be the subsets?

S1= {{B}, B}

S2= {{B}}

I'm not sure is S1 is both and how to write it and if S2 will keep both brackets?

Thanks for your help!!

In set notation, elements in a set are separated by commas.

So S1 is a set containing the elements B and {B} (which is itself a set containing B).

A subset of a set A is a set containing elements that are in A.

So {B} is a subset of S1 because {B} is a set containing only the element B. And B is an element of S1.

{{B}} is also a subset of S1. This is because {{B}} is a set containing only the element {B} and {B} is an element of S1.

Does that help? So what are all the subsets of S1 and S2? Remeber that the empty set {} is a subset of any set so you'll need to include the empty set in your list of subsets.

Reply 3

OP

Original post by notnek

In set notation, elements in a set are separated by commas.

So S1 is a set containing the elements B and {B} (which is itself a set containing B).

A subset of a set A is a set containing elements that are in A.

So {B} is a subset of S1 because {B} is a set containing only the element B. And B is an element of S1.

{{B}} is also a subset of S1. This is because {{B}} is a set containing only the element {B} and {B} is an element of S1.

Does that help? So what are all the subsets of S1 and S2? Remeber that the empty set {} is a subset of any set so you'll need to include the empty set in your list of subsets.

Yes that's really helped thanks! So the subsets of S1 are {B} and {{B}} and S2 {{B}} I believe?

Reply 4

OP

I just thought of another quick question actually. For S1={{B}, B} what will the cardinality be if we have another set which is S3= B= {e,f,g}?

Would it be 4 or would it be 2?

Reply 5

Original post by loryn95

Yes that's really helped thanks! So the subsets of S1 are {B} and {{B}} and S2 {{B}} I believe?

Those are correct subsets but you've missed a few.

A subset can have more than 1 element.

S1 contains B and {B} so you can make a subset with both of these elements:

{B, {B}}

For any set, one of the susbets of it will be the set itself.

Also, as I mentioned above, the empty set { } is a subset of any set.

Reply 6

Original post by loryn95

I just thought of another quick question actually. For S1={{B}, B} what will the cardinality be if we have another set which is S3= B= {e,f,g}?

Would it be 4 or would it be 2?

Can you clarify your question - which set do you want to know the cardinality of?

Reply 7

OP

Original post by notnek

Can you clarify your question - which set do you want to know the cardinality of?

Yeah sorry, I meant what is the cardinality of S1?
Is it |S1| 1 or |S1|4?

We know B has 3 members due to S3 which is why I was wondering whether we take this into account if B is within another set?

Reply 8

Original post by loryn95

Yeah sorry, I meant what is the cardinality of S1?
Is it |S1| 1 or |S1|4?

We know B has 3 members due to S3 which is why I was wondering whether we take this into account if B is within another set?

The cardinality of a set is how many elements are in the set.

S1 = {{B}, B}

As I explained before, this is a set containing only the elements {B} and B (since these are separated by commas).

So the cardinality is 2 because there are only 2 elements. What these elements are is irrelevant.

Reply 9

OP