Question

quais são os subconjuntos de A{1,2,3,4,5,6,}?

Answer 1

Como o conjunto $A$ tem $6$ elementos, então o total de subconjuntos que $A$ possui é

$2^{6}=64\text{ subconjuntos}$

$\begin{array}{clc} \{& \varnothing,\;\{1\},\,\{2\},\,\{3\},\,\{4\},\,\{5\},\,\{6\},\,\\ \\ &\{1,\,2\},\,\{1,\,3\},\,\{1,\,4\},\,\{1,\,5\},\,\{1,\,6\},\,\\ \\ &\{2,\,3\},\,\{2,\,4\},\,\{2,\,5\},\,\{2,\,6\},\,\\ \\ &\{3,\,4\},\,\{3,\,5\},\,\{3,\,6\},\,\\ \\ &\{4,\,5\},\,\{4,\,6\},\,\\ \\ &\{5,\,6\}\\ \\ &\{1,\,2,\,3\},\,\{1,\,2,\,4\},\,\{1,\,2,\,5\},\,\{1,\,2,\,6\},\,\\ \\ &\{1,\,3,\,4\},\,\{1,\,3,\,5\},\,\{1,\,3,\,6\},\,\\ \\ &\{1,\,4,\,5\},\,\{1,\,4,\,6\}\\ \\ &\{1,\,5,\,6\} \end{array}$

$\begin{array}{clc} &\{2,\,3,\,4\},\,\{2,\,3,\,5\},\,\{2,\,3,\,6\},\,\\ \\ &\{2,\,4,\,5\},\,\{2,\,4,\,6\},\,\\ \\ &\{2,\,5,\,6\},\,\\ \\ &\{3,\,4,\,5\},\,\{3,\,4,\,6\},\,\\ \\ &\{3,\,5,\,6\},\,\\ \\ &\{4,\,5,\,6\},\,\\ \\ &\{1,\,2,\,3,\,4\},\,\{1,\,2,\,3,\,5\},\,\{1,\,2,\,3,\,6\},\,\\ \\ &\{1,\,2,\,4,\,5\},\,\{1,\,2,\,4,\,6\},\,\\ \\ &\{1,\,2,\,5,\,6\},\,\\ \\ &\{1,\,3,\,4,\,5\},\,\{1,\,3,\,4,\,6\},\,\{1,\,3,\,5,\,6\},\,\\ \\ &\{1,\,4,\,5,\,6\},\, \end{array}$

$\begin{array}{clc} &\{2,\,3,\,4,\,5\},\,\{2,\,3,\,4,\,6\},\,\\ \\ &\{2,\,3,\,5,\,6\},\,\\ \\ &\{2,\,4,\,5,\,6\},\,\\ \\ &\{3,\,4,\,5,\,6\},\,\\ \\ &\{1,\,2,\,3,\,4,\,5\},\,\{1,\,2,\,3,\,4,\,6\},\,\\ \\ &\{1,\,2,\,3,\,5,\,6\},\,\\ \\ &\{1,\,2,\,4,\,5,\,6\},\,\\ \\ &\{1,\,3,\,4,\,5,\,6\},\,\\ \\ &\{2,\,3,\,4,\,5,\,6\},\,\\ \\ &\{1,\,2,\,3,\,4,\,5,\,6\}&\} \end{array}$