Understanding Rational and Irrational Sets

Hard Number And Operations Rational And Irrational Numbers

Consider a set of numbers defined as follows:

Let the set S be the union of the set of all rational numbers and the set of all irrational numbers.

Determine which of the following statements is true regarding the elements of the set S and their rationality:

All elements of the set S are rational numbers.

All elements of the set S are irrational numbers.

Every element of set S is either rational or irrational, but not both.

The set S contains only integers.

The set S is empty.

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