Question

Cardinalul m={x|x€N,x=3n-4,n€N,x<25

Answer 1

$M=\left \{ x\:|\:x\:\in\:\mathbb{N},x= 3n-4,n\:\in\:\mathbb{N},x<25\right \}$

$pt. \: n = 0 = > x = 3 \times 0 - 4 = - 4 \: \notin \: \mathbb{N}$

$pt. \: n = 1 = > x = 3 \times 1 - 4 = - 1 \: \notin \: \mathbb{N}$

$pt. \: n = 2 = > x = 3 \times 2 - 4 = 2 \: \in \: \mathbb{N}$

$pt. \: n = 3 = > x = 3 \times 3 - 4 = 5 \: \in \: \mathbb{N}$

$pt. \: n = 4 = > x = 3 \times 4 - 4 = 8 \: \in \: \mathbb{N}$

$pt. \: n = 5 = > 3 \times 5 - 4 = 11 \: \in \: \mathbb{N}$

$pt. \: n = 6 = > x = 3 \times 6 - 4 = 14 \: \in \: \mathbb{N}$

$pt. \: n = 7 = > 3 \times 7 - 4 = 17 \: \in \: \mathbb{N}$

$pt. \: n = 8 = > x = 3 \times 8 - 4 = 20 \: \in \: \mathbb{N}$

$pt. \: n = 9 = > x = 3 \times 9 - 4 = 23 \: \in \: \mathbb{N}$

$= > x\: \in \: \left \{ 2,5,8,11,14,17,20,23 \right \}$

$= > M=\left \{ 2,5,8,11,14,17,20,23 \right \}$

$=>cardM=8$