Question 3: Write two proper subsets of each of the following sets:
\((v)\) \(\;\) \(\{x|x\in Q\land 0< x\leq 2\} \)
Solution:
Two Proper Subsets are:
\( (i) \; \) \(\{1\}\)
\( (ii) \; \) \(\{2\}\)
Explanation:
The set contains all rational numbers greater than \(0\) and less than or equal to \(2\).
A proper subset of a set is a subset that is not equal to the original set.
The subsets \(\{1\}\) and \(\{2\}\) both contain some (but not all) elements of the original set.