Question

determinati cardinalul multimii a , unde a= { x apartine lui n mare dupa bara dreapta 2 la 2006 < 2x - 2 < 2 la 2007 }

Answer 1

[tex]2^{2006}\ \textless \ 2x-2\ \textless \ 2^{2007}|:2\\ 2^{2005}\ \textless \ x-1\ \textless \ 2^{2006}|+1\\ 2^{2005}+1\ \textless \ x\ \textless \ 2^{2006}+1\\ x\in\{2^{2005}+2;2^{2005}+3;...;2^{2005}+2^{2005}=2^{2006}\}\\ Multimea\ A \ va \ avea\ cardinalul\ 2^{2005}-1.[/tex]