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# Getting confused with sets- pls help!

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1. Hi guys!

I'm not sure with some answers for the following 5 sets, it would be amazing if someone could help! I'm mainly getting confused with the bracketing.

So the Sets are:

S1= {{B}, B}
S2={{B}}
S3={B}
S4=B={e,f,g}

And the questions I have...

1. What is the cardinality of S1?
I thought it would be 4, as the second B is equivalent to S4 which means it has 4 members. My friend however thinks its 2!

2. What is the Union of S1 and S2? I thought it might be S1US2= {{B}, B, {{B}}}.

3.What is the complemet of S1 in S2? S2\S1 = {{B}} or nothing?

4. What are the subsets of S1? Is it both {A} and A or only {A}? I think it is {A} because this only contains 1 member but I'm unsure!

5. Which are the subsets of S2? Do I write {{A}} or {A}? I know a set can be a subset of itself but do I leave the outer brackets or keep them on?

Thanks soo so much in advance! Really feel like I'm struggling a bit and we have a test tomorrow so any help is much appreciated!
2. [QUOTE=loryn95;68071736]
So the Sets are:

S1= {{B}, B}
S2={{B}}
S3={B}
S4=B={e,f,g}

And the questions I have...

1. What is the cardinality of S1?
I thought it would be 4, as the second B is equivalent to S4 which means it has 4 members. My friend however thinks its 2!
Your friend is right. {B} is an element of S1, it only counts as one element, even if it's a set in its own right, it's still just one element. So there are 2 elements in S1.

2. What is the Union of S1 and S2? I thought it might be S1US2= {{B}, B, {{B}}}.
Huh? S1 is the set containing the elements {B} and B. S2 is the set containing the element {B} (it's a subset of S1). So the uniion is the set containing {B} and B and {B}. But note that {B} is the same as {B], to state the obvious. So S1 U S2 = {{B}, B}.

3.What is the complemet of S1 in S2? S2\S1 = {{B}} or nothing?

What do you think? What are the elements that are in S2 but not in S1? Is {B} in both S2 and S1? See above...

4. What are the subsets of S1? Is it both {A} and A or only {A}? I think it is {A} because this only contains 1 member but I'm unsure!
Where did A come from? There are two elements, so you know that there are 4 subsets. One is the set itself, the other is the empty set. Then the other two are just sets containing single elements.

5. Which are the subsets of S2? Do I write {{A}} or {A}? I know a set can be a subset of itself but do I leave the outer brackets or keep them on?
Remember that the empty set is a subset of everything, and you need to keep the inner brackets.

Thanks soo so much in advance! Really feel like I'm struggling a bit and we have a test tomorrow so any help is much appreciated!
You really need to get used to the idea of a set being an element in another set, it may help you to write C = {B} and hence S1 = {C, B} or something like that to help cement that idea in your mind.

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Updated: October 17, 2016
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