Question

determine AÙB, onde A={xe R, -4 <×<3} e B={xe R, 1 <×< 9}​

Answer 1

Resposta:

Olá boa noite!

A = { -1 < x <3}

B = { 1 < x < 9}

A união entre A e B é o intervalo comum:

A U B = { x E R | x < 1 x < 9}

Observe que unindo A e B, todo intervalo A e B, é reunido

Answer 2

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⠀⠀☞ A união do conjunto A e B é o intervalo (-4) < x < 9. ✅  

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➡️⠀Vamos verificar os dois intervalos A e B através de retas numéricas:

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$\sf\blue{A:}~~~~~\begin{array}{l}\sf\green{\blacktriangleleft\!\!\textsf{------}\!\!\!\!\!\underset{\blue{(-4)}}\circ\!\!\!\!\!\textsf{-------}\!\!\!\!\!\underset{\blue{0}}\bullet\!\!\!\!\!\textsf{------}\!\!\underset{\blue{3}}\circ\!\!\textsf{------------------------}\!\!\blacktriangleright}\end{array}$

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$\sf\blue{B:}~~~~~\begin{array}{l}\sf\green{\blacktriangleleft\!\!\textsf{---------------}\!\!\underset{\blue{1}}\circ\!\!\textsf{-----------------------}\!\!\underset{\blue{9}}\circ\!\!\textsf{---}\!\!\blacktriangleright}\end{array}$

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⚡ " -Qual é a união destes dois intervalos?"

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$\sf\blue{A \cup B:}\begin{array}{l}\sf\green{\blacktriangleleft\!\!\textsf{-----}\!\!\!\!\!\underset{\blue{(-4)}}\circ\!\!\!\!\!\textsf{-------}\!\!\!\!\!\underset{\blue{0}}\bullet\!\!\!\!\!\textsf{--------------------------}\!\!\underset{\blue{9}}\circ\!\!\textsf{---}\!\!\blacktriangleright}\end{array}$

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➡️⠀Ou seja, a união destes dois intervalos será o intervalo [-4, 9[, ou seja:

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$\large\green{\boxed{\rm~~~\gray{A \cup B}~\pink{=}~\blue{ x \in \{-4 < x < 9\} }~~~}}$ ✅

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

⠀⠀☀️ Leia mais sobre união e intersecção de conjuntos:

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✈ https://brainly.com.br/tarefa/38027890

$\bf\large\red{\underline{\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

⠀⠀⠀⠀☕ $\Large\blue{\text{\bf Bons~estudos.}}$

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($\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

❄☃ $\sf(\purple{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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$\Huge\green{\text{ \underline{\red{\mathbb{S}}\blue{\mathfrak{oli}}~}~\underline{\red{\mathbb{D}}\blue{\mathfrak{eo}}~}~\underline{\red{\mathbb{G}}\blue{\mathfrak{loria}}~} }}$ ✞

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