Precalculus (10th Edition)

$0$ element: $\{\}.$ $1$ element: $\{a\}, \{b\}, \{c\}, \{d\}, \{e\}$ $2$ elements $\{a,b\}, \{a,c\}, \{a,d\}, \{a,e\}, \{b,c\}, \{b,d\} , \{b,e\}, \{c,d\}, \{c,e\}, \{d,e\}$ $3$ elements $\{a,b,c\}, \{a,b,d\}, \{a,b,e\}, \{a,c,d\}, \{a,c,e\}, \{a,d,e\}, \{b,c,d\}, \{b,c,e\}, \{b,d,e\}, \{c,d,e\}$ $4$ elements $\{a,b,c,d\}, \{a,b,c,e\}, \{a,b,d,e\}, \{a,c,d,e\}, \{b,c,d,e\}$ $5$ elements $\{a,b,c,d,e\}$
The set has $5$ elements so the set has $2^5=32$ subssets. These are: $0$ element: $\{\}.$ $1$ element: $\{a\}, \{b\}, \{c\}, \{d\}, \{e\}$ $2$ elements $\{a,b\}, \{a,c\}, \{a,d\}, \{a,e\}, \{b,c\}, \{b,d\} , \{b,e\}, \{c,d\}, \{c,e\}, \{d,e\}$ $3$ elements $\{a,b,c\}, \{a,b,d\}, \{a,b,e\}, \{a,c,d\}, \{a,c,e\}, \{a,d,e\}, \{b,c,d\}, \{b,c,e\}, \{b,d,e\}, \{c,d,e\}$ $4$ elements $\{a,b,c,d\}, \{a,b,c,e\}, \{a,b,d,e\}, \{a,c,d,e\}, \{b,c,d,e\}$ $5$ elements $\{a,b,c,d,e\}$