Answer to Question #319722 in Discrete Mathematics for Ice

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

$Power\,\,set\,\,is\,\,the\,\,set\,\,of\,\,all\,\,subsets\\a:2^{\left\{ a \right\}}=\left\{ \emptyset ,\left\{ a \right\} \right\} \\b:2^{\left\{ a,b \right\}}=\left\{ \emptyset ,\left\{ a \right\} ,\left\{ b \right\} ,\left\{ a,b \right\} \right\} \\c:2^{\left\{ \emptyset ,\left\{ \emptyset \right\} \right\}}=\left[ \begin{array}{c} in\,\,the\,\,previous\,\,answer\\ substitute\,\,a\,\,with\,\,\emptyset\\ and\,\,b\,\,with\,\,\left\{ \emptyset \right\}\\\end{array} \right] =\left\{ \emptyset ,\left\{ \emptyset \right\} ,\left\{ \left\{ \emptyset \right\} \right\} ,\left\{ \emptyset ,\left\{ \emptyset \right\} \right\} \right\}$