Subsets of sets

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    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!!
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    (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!!
    Lets take a slightly different case:

    Suppose S={a,b}

    Then the subsets are sets consisting of different combinations of elements of S.
    i.e. {a} {b} {a,b} and {}.............................. ..(1)

    Note that the whole set and the empty set are always subsets of our given set.

    Now suppose instead of the element "a", be have a set "{c}", I.e. S={{c},b}
    As far as the set S is concerned "{c}" is just an element of S. Note, "c" is NOT and element of S.
    We can just replace "a" with "{c}" in (1) and we have all the subsets of our new S.

    Can you now do your original question?
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    (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.
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    (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?
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    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?
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    (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.
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    (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?
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    (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?
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    (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.
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    Okay, thanks for your help!
 
 
 
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