Question

pls ex 15 plsssssssssssssssssssssssssssssssssssssssss va rog mult

Answer 1

Explicație pas cu pas:

a)

$x \leqslant 20 \implies x \in \{0, 1, 2, ..., 20\}$

$6 | (10 + x) \iff 6 \in \mathcal{D}_{10 + x} \iff (10 + x) \in \mathcal{M}_{6}$

$x \in \{2, 8; 14; 20\} \implies A = \{2, 8; 14; 20\}$

b)

$x \ \ \vdots \ 2 \implies b \in \{0, 2, 4, 6, 8\}$

$x \ \ \vdots \ 3 \implies (2+a+4+b) \ \ \vdots \ 3 \\ \iff (a+b+6) \ \ \vdots \ 3 \implies (a+b) \ \ \vdots \ 3$

b = 0 => a : 3 => a ∈ {0;3;6;9}

b = 2 => (a+2) : 3 => a ∈ {1;4;7}

b = 4 => (a+4) : 3 => a ∈ {2;5;8}

b = 6 => (a+6) : 3 => a ∈ {0;3;6;9}

b = 8 => (a+8) : 3 => a ∈ {1;4;7}

=> B = {2040; 2340; 2640; 2940; 2142; 2442; 2742; 2244; 2544; 2844; 2046; 2346; 2646; 2946; 2148; 2448; 2748}