List all the subsets of {1}.

Question

zehanz · Answer

Remember that every set is also a subset of itself.
Also the empty set is a subset of every set...
There is not much left to think about now!

anonymous · Answer

so it is 1

zehanz · Answer

Hmm, (...counting...) no, it is 2!

anonymous · Answer

oh so it is 1 and 2 or just 2

zehanz · Answer

Listing of all the subsets of {1}:

{1}
The emptyset

I think this listing is the answer.

anonymous · Answer

so {{}, {1}}

zehanz · Answer

Oh, I understand now, you are not supposed to just mention all the subsets, you have to give the set of all subsets of {1}. This is indeed:$$\left\{ \emptyset, \left\{ 1 \right\} \right\}$$

zehanz · Answer

Did you now that the number of subsets of a set is 2^(no of elements in the set)?

anonymous · Answer

No. my teacher put this on a study guide for a test and didnt teach it

zehanz · Answer

Impress/embarass him/her by asking this as a question ;)

Another thing: the no of elements in a set is called the Cardinal number.

Cardinal number of A={1, 2, 3} is 3. There are 8 subsets of A, because 2^3 = 8.
The set of all subsets of A is:$$\left\{ \emptyset, \left\{ 1 \right\} , \left\{ 2 \right\},\left\{ 3 \right\},\left\{ 1,2 \right\},\left\{ 1,3 \right\},\left\{ 2,3 \right\},\left\{ 1,2,3 \right\}\right\}$$