A={x€N|x=4-n,n€N stelar}​

Răspuns:

[tex]A = \{0,1,2,3\}[/tex]

Explicație pas cu pas:

[tex] A = \{ x\in \mathbb{N} | x = 4-n, n\in \mathbb{N}^*\}\\ x \in \mathbb{N} \implies 4-n \in \mathbb{N} \\\\\implies 4-n \geq 0 \implies 4 \geq n \implies n \leq 4, n \in \mathbb{N}^* \\\\\implies 0 < n \leq 4\\\\n = 1 \implies x = 4-1 = 3\\\\ n = 2 \implies x = 4-2 = 2\\\\ n = 3 \implies x = 4 - 3 = 1\\\\ n = 4 \implies x = 4-4 = 0\\\\ A = \{0,1,2,3\}[/tex]

N={0; 1; 2; 3; 4; ...}

N*={1; 2; 3; 4; ....}

Observi ca atunci cand apare "steluta" langa multimile N, Z, Q, R, atunci multimile respective nu il contin pe 0.

A={x€N|x=4-n,n€N*}

Din x€N => x>=0 => 4-n>=0 => 4>=n

Dar n€N*

=> n poate avea valorile 1, 2, 3 sau 4

n=1 => x=4-1=3

n=2 => x=4-2=2

n=3 => x=4-3=1

n=4 => x=4-4=0

Cum multimea A este formata din totalitatea numeleor naturale x care satisfac conditiile respective.

A={0; 1; 2; 3}