Question

Find the power set of the set {Ø , { Ø }, a, b, c} where a, b and c are distinct elements.

Answer 1

For the set $A=\{Ø , \{ Ø \}, a, b, c\}$ the power set contains the following $2^5=32$ subsets:

$P(A)=\bigg\{Ø, \big\{Ø\big\}, \big\{ \{Ø\} \big\}, \big\{a\big\}, \big\{b\big\}, \big\{c\big\}, \\ \big\{Ø, \{Ø\}\big\}, \big\{Ø, a\big\}, \big\{Ø, b\big\}, \big\{Ø, c\big\}, \big\{\{Ø\}, a\big\}, \\ \big\{\{Ø\}, b\big\}, \big\{\{Ø\}, c\big\},\big\{a, b\big\}, \big\{a, c\big\}, \big\{b, c\big\}, \\ \big\{Ø, \{Ø\}, a\big\}, \big\{Ø, \{Ø\}, b\big\}, \big\{Ø, \{Ø\}, c\big\}, \\ \big\{Ø, a, b\big\}, \big\{Ø, a, c\big\}, \big\{Ø, b, c\big\}, \big\{\{Ø\}, a, b\big\}, \\ \big\{\{Ø\}, a, c\big\}, \big\{\{Ø\}, b,c\big\}, \big\{a, b, c\big\}, \big\{Ø, \{Ø\}, a, b\big\}, \\ \big\{Ø, \{Ø\}, a, c\big\}, \big\{Ø, \{Ø\}, b, c\big\}, \big\{Ø, a, b, c\big\}, \\ \big\{\{Ø\}, a, b, c\big\}, \big\{Ø, \{Ø\}, a, b, c\big\} \bigg\}$