Question

Fie A= { 1,2,3,4...99,100 }. Determinati numarul submultimilor B ⊂ A, stiind ca { 1,2 } ⊂ B ⊂ { 1,2... 81 }

Answer 1

Multimea B poate fi:
- cu 2 elemente B={1,2}-o multime
-cu 3 elemente B={1,2,3},B={1,2,4},...,B={1,2,81}-79 multimi
-cu 4 elemete B={1,2,3,4),B={1,2,3,5}....,B={1,2,80,81}-78+77+...+1=79*78/2 multimi
..........
-cu 81 elemente B={1,2,3,..81}- o multime
Numarul total de submultimi este:
$C_{79}^0+C_{79}^1+...+C_{79}^{79}=2^{79}\ submultimi$