Question

A subset of a power set. (a) Let X = {a, b, c, d}. What is...

A subset of a power set.

(a)

Let X = {a, b, c, d}. What is { A: A ∈ P(X) and |A| = 2 }?

comment: Please give a clear explanation to what this set builder notation translate to? Because I've checked the answer for a) and it is A= {{a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}}.

I don't understand because the cardinality of A has to be 2 right? Meanwhile, the answer is basically saying there's 6 elements. So like therefore the cardinality of A became 6. So isn't the answer wrong? Or am I missing the point of the set builder notation?

(b)

Let A = {1, 2, 3}. What is {X ∈ P(A): 2 ∈ X}?

Comment: This one too, I don't understand how to translate the set builder notation. Like I checked and the answer to this question is something to do with every set that has 2 in them. So like why?

Final comment: I think what I'm lost is that what is X actually? Is it a set or a power set or what? Thank you,

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