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**PhizKid** Does this mean that whenever the function P(x) is true, then x is an element of X, and when P(x) is false, then x is not an element of X?

I'm confused because the wording says that "...a sentence P(x) that is either true or false whenever x is any particular element of X..." which leads me to believe that whether P(x) is either true or false, then it is still an element of set X.

Or is it saying that there is a set within X in which P(x) is true, and there is also another set within X in which P(x) is false?