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  1. e , o conjunto é o intervalo

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Answer

A interseção é o intervalo .

Solution

  1. Primeiro, identificamos os intervalos dados:
  2. A interseção contém os números que pertencem a ambos os conjuntos. Assim, devemos satisfazer as duas condições simultaneamente:
  3. Para encontrar a interseção, analisamos as condições dos limites:
    • O limite inferior será o maior entre e , ou seja, .
    • O limite superior será o menor entre e , ou seja, .
  4. Além disso, notamos que:
    • Em , é estritamente menor que .
    • Em , pode ser igual a , pois .
    Portanto, a interseção é:
  5. Comparando com as opções dadas, percebemos que a opção correspondente é:
Portanto, a resposta correta é a opção a).

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The Deep Dive

Vamos analisar os conjuntos.
O conjunto representa todos os números que estão entre -1 e 2, sem incluir os extremos. Já o conjunto inclui todos os números que vão de 0 a 3, incluindo 0, mas não 3.
Agora, para encontrar a interseção , precisamos identificar os valores que pertencem a ambos os conjuntos. O intervalo de A é e o intervalo de B é . A interseção desses intervalos é onde eles se sobrepõem, que é:
Portanto, a resposta correta é a opção a) .

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