 # What do the parenthesis mean in the set builder notation <mo fence="false" stretchy="false">{ ziphumulegn 2022-07-01 Answered
What do the parenthesis mean in the set builder notation $\left\{\left(x,S\right)\mid x\in S,S\in {2}^{A}\right\}$
I've looked around but can't quite figure out what the set produced by the builder notation in the title would actually look like - specifically, what element does (x,S) actually yield? If someone could explain what the output of the statement would look like I would really appreciate it, thank you.
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Step 1
The parentheses in (x, S) tell you that the elements of the set you are building are ordered pairs. In your example A is some set, and ${2}^{A}$ is the set of all its subsets.
Step 2
Pick a simple example, say $A=\left\{1,2\right\}$ and write out all the elements of the set you are building to see what is going on.

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