Write Down All Possible Subsets of Given Sets
Write down all possible subsets of each of the following sets:
(i) \(\{a\}\)
(ii) \(\{0,1\}\)
(iii) \(\{a,b,c\}\)
(iv) \(\{1,\{1\}\}\)
(v) \(\{\Phi\}\)
Solution
(i) Subsets of \[ \{a\} \] are \[ \Phi,\ \{a\} \]
(ii) Subsets of \[ \{0,1\} \] are \[ \Phi,\ \{0\},\ \{1\},\ \{0,1\} \]
(iii) Subsets of \[ \{a,b,c\} \] are \[ \Phi,\ \{a\},\ \{b\},\ \{c\}, \] \[ \{a,b\},\ \{a,c\},\ \{b,c\},\ \{a,b,c\} \]
(iv) Subsets of \[ \{1,\{1\}\} \] are \[ \Phi,\ \{1\},\ \{\{1\}\},\ \{1,\{1\}\} \]
(v) Subsets of \[ \{\Phi\} \] are \[ \Phi,\ \{\Phi\} \]