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# Trouble understanding these sets!

Sun 16 Oct, 2016 04:08 am
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!
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Kolyo

1
Sun 16 Oct, 2016 02:39 pm
@jessicalorynn,
jessicalorynn wrote:

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!

There are 2 elements, {B} and B. The cardinality is 2.

Quote:

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

No {{B}} is not an element of S2. It is S2.

Quote:

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

Empty set. {}. This is a set with no elements -- cardinality zero.

Quote:

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!

S1 has 2 elements, so it has 2^2 = 4 subsets.

They are {}, {{B}}, {B}, {{B},B}.

Quote:

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?

S2 has 1 element. So it has 2^1 = 2 subsets.

They are {} and {{B}}.
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