Question

Daca A={x e Z| |x|<4}si B={x e Z*+|-x+2>-5},calculati AUB si A\B

Answer 1

Răspuns:

Explicație pas cu pas:

A=(-4;4)∩Z= {-3;-2....2;3}

pt B avem -x>-7

deci x<7

B=(-∞;7)∩Z={...-5;-4;-3....5;6}

se observa ca A⊂B

deci

A∪B=B si A\B=∅

Answer 2

Răspuns:

AUB ; A\B

Explicație pas cu pas:

$A = \Big\{x \in \mathbb{Z} \Big| |x| < 4 \Big\}$

$|x| < 4 \iff - 4 < x < 4$

$\implies A = \Big\{-3; -2; -1; 0; 1; 2; 3\Big\}$

$B = \Big\{x \in \mathbb{Z_{+}^{\ast}} \Big| - x + 2 > - 5 \Big\}$

$- x + 2 > - 5 \iff - x > - 5 - 2 \\ - x > - 7 \ \Big|_{\cdot (-1)} \implies x < 7$

$\implies B = \Big\{1; 2; 3; 4; 5; 6\Big\}$

atunci:

$A \cup B = \Big\{-3; -2; -1; 0; 1; 2; 3; 4; 5; 6\Big\}$

$A - B = \Big\{-3; -2; -1; 0\Big\}$