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All rational numbers are real so the phrase "real rational" has no meaning.

There are an infinite number of subsets:

The emply or null set,

{1,1.5, 7/3},

{2},

(0.1,0.2,0.3,0.66..., 5.142857142857...} are some examples.

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Q: Which are the subsets of real rational numbers?
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