Is Option 2 the Only Subset of P(C) in This List?

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Horizyn
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Hi everyone,

I'm new here. Doing a CS degree and started a Theoretical Computer Science I module beginning second semester.

Need to hand in an assignment at the end of this month.

I've answered all the questions so far, except one I'm unsure about.

I'd appreciate your help and feedback on this one.

The question follows:

Which one of the following is a subset of P(C)?

1. {{1,2}}
2. {{a,b}}
3. {a,b}
4. {{a},{1,2}}

The question is based on the following sets, where U represents a universal set:

U={a,b, {a,b},{1},{2},{1,2}}; C={a,b,{a,b},{1,2}}

It doesn't make sense to me, since I've figured that 1,2 & 3 are all subsets of P(C). I'm not sure if the question is asking for more than one choice, even though it says which ''one'' of the following. If it asked which one of the following is ''not'' a subset of P(C), it would make more sense as it would have been option 4.

This is the first time I've been exposed to Discrete Mathematics, so excuse me if things aren't too obvious for me.

Thanks guys!

Correction: Changed - U={a,b {a,b},{1},{2},{1,2}} to U={a,b,{a,b},{1},{2},{1,2}}
 
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I agree with you. It looks like the word "not" is missing from the question.
 
Usually the hint is "Back to the definition."

Exactly what is the precise definition of P(set)?

And then can you, because C is small enough, construct P(C) from that definition and then produce all the subsets of P(C)?
 
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However, you are mistaken in thinking that {a, b} is a subset of P(C).
 
HallsofIvy said:
However, you are mistaken in thinking that {a, b} is a subset of P(C).

{a,b} certainly is a subset of P(C) since a and b are subsets of C.
 
We were told in the original post that C={a,b,{a,b},{1,2}}.

a and b are NOT subsets of that set.
 
I had to read over power sets again, but it turns out you're right, Halls. In fact, the question by the OP isn't posed incorrectly at all. Given

C = { a, b, {a,b}, {1,2} }

then

P(C) = { {}, {a}, {b}, {a,b}, {{a,b}}, {{1,2}}, ... }

Notice {a,b} is the collection of a and b from C, while {{a,b}} is the collection of {a,b} from C.

GIven the question

Which one of the following is a subset of P(C)?

1. {{1,2}}
2. {{a,b}}
3. {a,b}
4. {{a},{1,2}}

Looking at 1. that is the set that contains the element {1,2}, but P(C) doesn't contain {1,2}, it contains {{1,2}}.
Simiarly for the rest, so the answer is 2.