Question
a. \( A=\{x / x \in \mathbb{R} \wedge-2
Ask by Malone Griffin. in Peru
Mar 21,2025
Ask by Malone Griffin. in Peru
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
El conjunto \( A \) incluye todos los números reales entre \(-2\) y \(3\), sin incluir \(-2\) y \(3\).
Solution
- Sea el conjunto \( A = \{x \in \mathbb{R} \mid -2 < x < 3\} \).
- Esto significa que \( A \) contiene todos los números reales \( x \) que cumplen la condición \( -2 < x < 3 \).
- El intervalo \( (-2, 3) \) representa los números que están estrictamente entre \(-2\) y \(3\), sin incluir a los extremos.
- Por lo tanto, \( A = (-2, 3) \).
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Simplify this solution The Deep Dive
Did you know that the set \( A \) represents all real numbers between -2 and 3, excluding the endpoints? It’s like a cozy little neighborhood on the number line where all the numbers hang out but don't invite -2 and 3 to the party! In practice, this notation can be super useful for defining intervals in mathematics. For example, if you're analyzing a polynomial function, knowing that your variable \( x \) must lie within this range can help you predict the function's behavior, such as its roots or maximum and minimum values. Happy number exploring!
