P o w e r s e t i s t h e s e t o f a l l s u b s e t s a : 2 { a } = { ∅ , { a } } b : 2 { a , b } = { ∅ , { a } , { b } , { a , b } } c : 2 { ∅ , { ∅ } } = [ i n t h e p r e v i o u s a n s w e r s u b s t i t u t e a w i t h ∅ a n d b w i t h { ∅ } ] = { ∅ , { ∅ } , { { ∅ } } , { ∅ , { ∅ } } } 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\} P o w er se t i s t h e se t o f a ll s u b se t s a : 2 { a } = { ∅ , { a } } b : 2 { a , b } = { ∅ , { a } , { b } , { a , b } } c : 2 { ∅ , { ∅ } } = ⎣ ⎡ in t h e p re v i o u s an s w er s u b s t i t u t e a w i t h ∅ an d b w i t h { ∅ } ⎦ ⎤ = { ∅ , { ∅ } , { { ∅ } } , { ∅ , { ∅ } } }
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