Question 3: Write two proper subsets of each of the following sets:
\((v)\) \(\;\) \(R \)
Solution:
Two Proper Subsets are:
\( (i) \; \) \(Q\)
\( (ii) \; \) \({Q}’\)
Explanation:
The set of real numbers \(R\) is defined as the union of rational \(Q\) and irrational numbers \({Q}’\).
A proper subset of a set is a subset that is not equal to the original set.
The subsets \(Q\) and \({Q}’\) both contain some (but not all) elements of the original set.