Question

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Answer 1

a) A u B = R

c) A u B = (-infinit, 3]

b) A u B = N

d) A = [-1, 4] iar B = (-1, 1)

A u B = [-1, 4]

Answer 2

Explicație pas cu pas:

a)

$A \cup B = \mathbb{Q} \cup \mathbb{R} = \mathbb{R}$

b)

$A \cup B = \Big(0; +\infty\Big) \cup \mathbb{N} = \mathbb{N}$

c)

$A \cup B = \Big(-\infty; 2\Big) \cup \Big(-1; 3\Big] = \Big(-\infty; 3\Big]$

d)

$A = \Big[-1; 4\Big]$

$|x + 2| < 2 \iff -2 < x + 2 < 2 \\ \implies -4 < x < 0 \iff B = \Big(-4; 0\Big)$

$A \cup B = \Big[-1; 4\Big] \cup \Big(-4; 0\Big) = \Big(-4; 4\Big]$