Question

Find the power set of each of these sets, where a and b are distinct elements.

a) {a} b) {a, b} c) {∅, {∅}}

Answer 1

Let us find the power set of each of these sets, where $a$ and $b$ are distinct elements.

a) For the set $\{a\}$ its power set is $P(\{a\} )=\{\emptyset, \{a\} \}.$

b) For the set $\{a, b\}$ its power set is $P(\{a, b \} )=\{\emptyset, \{a\}, \{b\}, \{a, b\} \}.$

c) For the set $\{∅, \{∅\}\}$ its power set is $P(\{∅, \{∅\}\})=\{\emptyset,\{\emptyset \},\{\{\emptyset \}\},\{∅, \{∅\}\}\}.$