SOLUTION: Please help me enumerate all the subsets of C={x|x²=4} Thankyou

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Question 975673: Please help me enumerate all the subsets of C={x|x²=4} Thankyou
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Enumerating C you get

So, the subsets of C are:

The empty set because the empty set is a subset of every set.





And the set C itself,

John

My calculator said it, I believe it, that settles it

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
C = {x|x²=4}     <-- that's set-builder notation.

There are only two numbers whose squares are 4.  They are -2 and 2.

C = {x|x²=4} = {-2,2}   <-- that's roster notation.

If a set has n elements, it has 2n subsets.  So since C has 2 elements,
it has 22 or 4 subsets.  They are:

1. { } or ⌀ <-- the empty set, which is a proper subset of every set except itself.
2. {-2)    <-- a one-element set, which is called a singleton.
3. {2}     <-- another singleton subset.
4. {-2,2}  <-- the whole set C, which is not a PROPER subset, but still a subset. 

Edwin