Question 3: Write two proper subsets of each of the following sets:
\((i)\) \(\;\) \( \{a,b,c\}\)
Solution:
Two Proper Subsets are:
\( (i) \; \) \(\{a,b\}\)
\( (ii) \; \) \(\{b,c\}\)
Explanation:
All subsets are \(\phi,\)\(\{a\},\)\(\{b\},\)\(\{c\},\)\(\{a,b\},\)\(\{a,c\},\)\(\{b,c\},\) \(\{a,b,c\}\)
A proper subset of a set is a subset that is not equal to the original set.
So, we select any combination of elements from the set without including all of them.
The subsets \(\{a,b\}\) and \(\{b,c\}\) both contain some (but not all) elements of the original set.