Question

given the sets A=[x:x>-3] B=[-4,0) and C=[0,2] determine the following sets and represent them on the real line a AUB, b BUC, c AUC, d AUBUC

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Answer to a math question given the sets A=[x:x>-3] B=[-4,0) and C=[0,2] determine the following sets and represent them on the real line a AUB, b BUC, c AUC, d AUBUC

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Esmeralda
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101 Answers
Para representar los conjuntos en la recta real, primero debemos entender qué representan los conjuntos dados.

- El conjunto A = \{x: x > -3\} representa todos los números reales mayores que -3.
- El conjunto B = [-4,0) representa todos los números reales mayores o iguales a -4 pero menores que 0.
- El conjunto C = [0,2] representa todos los números reales mayores o iguales a 0 y menores o iguales a 2.

Ahora, vamos a determinar los siguientes conjuntos y a representarlos en la recta real:

a) A \cup B : Este conjunto representa todos los números reales que pertenecen a A o a B . Por lo tanto, es el conjunto de todos los números reales mayores que -3 o mayores o iguales a -4 pero menores que 0. Entonces, el conjunto A \cup B = \{x: x > -4\} .

b) B \cup C : Este conjunto representa todos los números reales que pertenecen a B o a C . Por lo tanto, es el conjunto de todos los números reales mayores o iguales a -4 pero menores que 2. Entonces, el conjunto B \cup C = [-4,2) .

c) A \cup C : Este conjunto representa todos los números reales que pertenecen a A o a C . Por lo tanto, es el conjunto de todos los números reales mayores que -3 o mayores o iguales a 0 pero menores o iguales a 2. Entonces, el conjunto A \cup C = \{x: x > -3\} .

d) A \cup B \cup C : Este conjunto representa todos los números reales que pertenecen a A , B o a C . Por lo tanto, es el conjunto de todos los números reales mayores que -4. Entonces, el conjunto A \cup B \cup C = \{x: x > -4\} .

Respuestas:
- a) A \cup B = \{x: x > -4\}
- b) B \cup C = [-4,2)
- c) A \cup C = \{x: x > -3\}
- d) A \cup B \cup C = \{x: x > -4\}

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