IP2U10 HOT Q2

Consider the following sets:
The set of natural numbers, \(\mathbb{N}\) ;
The set of integers, \(\mathbb{Z}\) ;
The set of rational numbers, \(\mathbb{Q}\) ;
The set of real numbers, \(\mathbb{R}\) .

1. Which of the above sets is/are such that \(\left\{ 0,\frac{1}{3} \right\}\) is a subset of it?
2. Give a description of the set \(\mathbb{R} \setminus \mathbb{Q}\) , i.e., the set that contains all elements that are in \(\mathbb{R}\) but not in \(\mathbb{Q}\).
   Hence write down a subset of \(\mathbb{R} \setminus \mathbb{Q}\).