# Correct reading of Set builder Notation?

could anyone please let me know the correct reading(sentence form) of set builder notation, confused with different interpretation in different resources.

Many Thanks

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The set $\{x\mid\varphi(x)\}$ is "The set of all $x$ such that $\varphi(x)$ holds." Note that sometimes such collection is not a set (e.g. the collection of all sets); and sometimes we wish to limit the elements to be taken from a certain set $A$.
The set $\{x\in A\mid\varphi(x)\}$ is "The set of all $x$ in $A$ such that $\varphi(x)$ is true."