Question

C={x apartine IN | 10 supra x+1 apartine IN }

Answer 1

$C=\left \{ x\:\in\:\mathbb{N}\:|\:\frac{10}{x+1}\:\in\:\mathbb{N} \right \}$

$\frac{10}{x + 1} \: \in \: \mathbb{N} = > (x + 1) \: \in \: D_{10}$

$D_{10}=\left \{ \pm1,\pm2,\pm5,\pm10 \right \}$

$1)x + 1 = - 1$

$x = - 1 - 1$

$x = - 2 \: \notin \: \mathbb{N}$

$2)x + 1 = 1$

$x = 1 - 1$

$x = 0 \: \in \: \mathbb{N}$

$3)x + 1 = - 2$

$x = - 2 - 1$

$x = - 3 \: \notin \: \mathbb{N}$

$4)x + 1 = 2$

$x = 2 - 1$

$x = 1 \: \in \: \mathbb{N}$

$5)x + 1 = - 5$

$x = - 5- 1$

$x = - 6 \: \notin \: \mathbb{N}$

$6)x + 1 = 5$

$x = 5 - 1$

$x = 4 \: \in \: \mathbb{N}$

$7)x + 1 = - 10$

$x = - 10 - 1$

$x = - 11 \: \notin \: \mathbb{N}$

$8)x + 1 = 10$

$x = 10 - 1$

$x = 9 \: \in \: \mathbb{N}$

$x \: \in \: \left \{ 0,1,4,9 \right \}$

$= > C=\left \{ 0,1,4,9 \right \}$