Write Down All Possible Proper Subsets of Given Sets
Write down all possible proper subsets of each of the following sets:
(i) \(\{1,2\}\)
(ii) \(\{1,2,3\}\)
(iii) \(\{1\}\)
Solution
(i) Proper subsets of \[ \{1,2\} \] are \[ \Phi,\ \{1\},\ \{2\} \]
(ii) Proper subsets of \[ \{1,2,3\} \] are \[ \Phi,\ \{1\},\ \{2\},\ \{3\}, \] \[ \{1,2\},\ \{1,3\},\ \{2,3\} \]
(iii) Proper subset of \[ \{1\} \] is \[ \Phi \]