Question 3: Write two proper subsets of each of the following sets:
\((v)\) \(\;\) \(Q \)
Solution:
Two Proper Subsets are:
\( (i) \; \) \(\{\frac{1}{2},\frac{1}{3},\frac{1}{4}\}\)
\( (ii) \; \) \(\{-\frac{1}{2},-\frac{1}{3},-\frac{1}{4}\}\)
Explanation:
The set of rational numbers \(Q\) consists of all numbers that can be written in the form \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q\ne 0\).
A proper subset of a set is a subset that is not equal to the original set.
The subsets \(\{\frac{1}{2},\frac{1}{2},\frac{1}{3}\}\) and \(\{-\frac{1}{2},-\frac{1}{2},-\frac{1}{3}\}\) both contain some (but not all) elements of the original set.