**Question:**

Write down all subsets of each of the following sets:

(i) $A=\{A\}$

(ii) $B=\{a, b\}$

(iii) $\mathrm{C}=\{-2,3\}$

(iv) $D=\{-1,0,1\}$

(v) $E=\phi$

(vi) $F=\{2,\{3\}\}$

(vii) $G=\{3,4,\{5,6\}\}$

**Solution:**

(i) The subsets of $\{\mathrm{A}\}$ are $\phi$ and $\{\mathrm{A}\}$

(ii) The subsets of $\{a, b\}$ are $\phi,\{a\},\{b\}$, and $\{a, b\}$.

(iii) The subsets of $\{-2,3\}$ are $\phi,\{-2\},\{3\}$, and $\{-2,3\}$.

(iv) The subsets of $\{-1,0,1\}$ are $\phi,\{-1\},\{0\},\{1\},\{-1,0\},\{0,1\},\{-1,1\},\{-1,0,1\}$

(v) $\phi$ has only one subset $\phi$.

(vi) let $x=\{3\}$

Then, $F=\{2, x\}$

The subsets of $\{2, x\}$ are $\phi,\{2\},\{x\},\{2, x\}$

i.e $\phi,\{2\},\{\{3\}\},\{2,\{3\}\}$

(vii) let $x=\{5,6\}$

Then, $G=\{3,4, x\}$

The subsets of $\{3,4, x\}$ are $\phi,\{3\},\{4\},\{x\},\{3, x\},\{4, x\},\{3,4\},\{3,4, x\}$

i.e. $\phi,\{3\},\{4\},\{\{5,6\}\},\{3,\{5,6\}\},\{4,\{5,6\}\},\{3,4\},\{3,4,\{5,6\}\}$