Răspuns:
Explicație pas cu pas:
Avem:
A: -5 ≤ x < 2
B: -4 ≤ x ≤ 4
c: -1 < x < 5.
AUBUC = [-5, 5)
AnB = [-4, 2) ,
AnC = (-1, 2),
BnC = (-1, 4],
AnBnC = (-1, 2),
A-C = [-5 -1],
B-C = [-4, -1],
C-A = [2, 5).
[tex]-5 \leq x < 2[/tex]
[tex]x \in \mathbb{Z} \implies \boldsymbol{A = \{-5;-4;-3;-2;-1;0;1\}}\\[/tex]
[tex]|x| \leq 4 \iff -4 \leq x \leq 4[/tex]
[tex]x \in \mathbb{Z} \implies \boldsymbol{B = \{-4;-3;-2;-1;0;1;2;3;4\}}\\[/tex]
[tex]|x-2| < 3 \iff - 3 < x - 2 < 3\ \ \Big|+2 \\[/tex]
[tex]-3 + 2 < x < 3 + 2 \iff -1 < x < 5[/tex]
[tex]x \in \mathbb{Z} \implies \boldsymbol{C = \{0;1;2;3;4\}}\\[/tex]
⇒
[tex]A \cup B \cup C = \{-5;-4;-3;-2;-1;0;1;2;3;4\}\\[/tex]
[tex]A \cap B = \{-4;-3;-2;-1;0;1\}[/tex]
[tex]A \cap C = \{0;1\}[/tex]
[tex]B \cap C = \{0;1;2;3;4\}[/tex]
[tex]A \cap B \cap C = \{0;1\}[/tex]
[tex]A - C = \{-5;-4;-3;-2;-1\}[/tex]
[tex]B - C = \{-4;-3;-2;-1\}[/tex]
[tex]C - A = \{2;3;4\}[/tex]
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Răspuns:
Explicație pas cu pas:
Avem:
A: -5 ≤ x < 2
B: -4 ≤ x ≤ 4
c: -1 < x < 5.
AUBUC = [-5, 5)
AnB = [-4, 2) ,
AnC = (-1, 2),
BnC = (-1, 4],
AnBnC = (-1, 2),
A-C = [-5 -1],
B-C = [-4, -1],
C-A = [2, 5).
Verified answer
[tex]-5 \leq x < 2[/tex]
[tex]x \in \mathbb{Z} \implies \boldsymbol{A = \{-5;-4;-3;-2;-1;0;1\}}\\[/tex]
[tex]|x| \leq 4 \iff -4 \leq x \leq 4[/tex]
[tex]x \in \mathbb{Z} \implies \boldsymbol{B = \{-4;-3;-2;-1;0;1;2;3;4\}}\\[/tex]
[tex]|x-2| < 3 \iff - 3 < x - 2 < 3\ \ \Big|+2 \\[/tex]
[tex]-3 + 2 < x < 3 + 2 \iff -1 < x < 5[/tex]
[tex]x \in \mathbb{Z} \implies \boldsymbol{C = \{0;1;2;3;4\}}\\[/tex]
⇒
[tex]A \cup B \cup C = \{-5;-4;-3;-2;-1;0;1;2;3;4\}\\[/tex]
[tex]A \cap B = \{-4;-3;-2;-1;0;1\}[/tex]
[tex]A \cap C = \{0;1\}[/tex]
[tex]B \cap C = \{0;1;2;3;4\}[/tex]
[tex]A \cap B \cap C = \{0;1\}[/tex]
[tex]A - C = \{-5;-4;-3;-2;-1\}[/tex]
[tex]B - C = \{-4;-3;-2;-1\}[/tex]
[tex]C - A = \{2;3;4\}[/tex]