The universal set for the set of rational numbers and the set of irrational numbers is
This basic set is called the Universal Set. The universal set is usually denoted by U, and all its subsets by the letters A, B, C, etc. For example, for the set of all integers, the universal set can be the set of rational numbers or, for that matter, the set R of real numbers. If we expand the set of integers to include all decimal numbers, we form the set of real numbers. The set of reals is sometimes denoted by R.
The set of rational numbers or irrational numbers is a subset of the set of real numbers.
Ex: The interval consists of all the numbers between the numbers two and three.
A [2,3] = {x:2 ≤ x ≤ 3}.
Then the rational numbers subsets of this set gets in universal subset of Real numbers as well as for irrational numbers as they are subset of Real Numbers set.