Question

quantos subconjuntos de N com apenas cinco elementos existem? dê três exemplos diferentes explicação

Answer 1

Se N possui 5 elementos, o número de subconjuntos é dado por $2^n$.

$2^n=\\2^5=\\\boxed{32}$


 Consideremos o conjunto N sendo $N=\left\{a,b,c,d,e\right\}$, segue que,

$P(N)=\begin{cases}\o,a,b,c,d,e\\\left\{a,b\right\},\left\{a,c\right\},\left\{a,d\right\},\left\{a,e\right\},\left\{b,c\right\},\left\{b,d\right\},\left\{b,e\right\},\left\{c,d\right\},\left\{c,e\right\},\left\{d,e\right\}\\\left\{a,b,c\right\}\left\{a,b,d\right\}\left\{a,b,e\right\},\left\{a,c,d\right\},\left\{a,c,e\right\},\left\{a,d,e\right\},\left\{b,c,d\right\},\left\{b,c,e\right\},\left\{b,d,e\right\},\left\{c,d,e\right\}\\\left\{a,b,c,d\right\}\left\{a,b,c,e\right\},\left\{a,b,d,e\right\},\left\{a,c,d,e\right\},\left\{b,c,d,e\right\}\\\left\{a,b,c,d,e\right\}\end{Bmatrix}$