Question 3: Write two proper subsets of each of the following sets:
\((iv)\) \(\;\) \(Z \)
Solution:
Two Proper Subsets are:
\( (i) \; \) \(\{1,2,3\}\)
\( (ii) \; \) \(\{-1,-2,-3\}\)
Explanation:
Since \(Z\) is an infinite set, it has infinitely many subsets and infinitely many proper subsets.
It is the set of integers, which includes both positive and negative numbers.
A proper subset of a set is a subset that is not equal to the original set.
The subsets \(\{1,2,3\}\) and \(\{-1,-2,-3\}\) both contain some (but not all) elements of the original set.