Question

Determinati numarul tuturor submultimilor multimii A={1,2}x{3,4,5}

Answer 1

$A = \{1,2\}\times \{3,4,5\} \\ \\ Notam cu | M| cardinalul unei multimi M. \\ \\ Stim ca: |M\times N| = |M|\cdot |N| \\ \\ \Rightarrow |A| = \Big|\{1,2\} \times \{3,4,5\}\Big| = \Big|\{1,2\}\Big|\cdot \Big|\{3,4,5\}\Big| = 2\cdot 3 = 6 \\ \\ \Rightarrow Multimea A are 6 elemente. \\ \\ \Rightarrow Numarul submultimilor multimii A este: \\ \\ C_6^{0}+C_6^1+C_6^2+...+C_6^6 = 2^6 =64$

Answer 2

A are 2*3=6 elemente (perechi ordonate)
deci 2^6=2³*2³=8*8=64 submultimi
as simple (and quick) as that!!