a. [tex]\bigg|\{a,b,\{a,b\}\}\bigg|=3\implies\bigg|\mathscr P\bigg(\{a,b,\{a,b\}\bigg)\bigg|=2^3=8[/tex]
b. [tex]\bigg|\{\varnothing,a,\{a\},\{\{a\}\}\}\bigg|=4\implies\bigg|\mathscr P\bigg(\{\varnothing,a,\{a\},\{\{a\}\}\}\bigg)\bigg|=2^4=16[/tex]
c. [tex]|\varnothing|=0\implies\bigg|\mathscr P(\varnothing)\bigg|=2^0=1\implies\bigg|\mathscr P(\mathscr P(\varnothing))\bigg|=2^1=2[/tex]
