7:21 PM Wed Jan 29 \( 22 \% \) Emilio Mejia Felic... G. 4 Unions and intersections of sets Video 05:28 Let \( J=\{x \mid x \geq-2\} \) and \( K=\{x \mid x<6\} \). What is \( J \cup K \) ? \[ \{-2,-1,0,1,2,3,4,5\} \] \[ \{x \mid-2 \leq x<6\} \] \( \{x \mid x \) is a real number \( \} \) Not ready yet?

To find the union of the sets \( J \) and \( K \), we first need to understand what each set represents. 1. **Set \( J \)**: \[ J = \{x \mid x \geq -2\} \] This means that \( J \) includes all real numbers that are greater than or equal to \(-2\). In interval notation, this can be expressed as: \[ J = [-2, \infty) \] 2. **Set \( K \)**: \[ K = \{x \mid x < 6\} \] This means that \( K \) includes all real numbers that are less than \( 6 \). In interval notation, this can be expressed as: \[ K = (-\infty, 6) \] 3. **Union of Sets \( J \) and \( K \)**: The union of two sets \( J \) and \( K \), denoted \( J \cup K \), includes all elements that are in either \( J \) or \( K \) or in both. To find \( J \cup K \), we combine the intervals: - The left endpoint of \( J \) is \(-2\) and it extends to infinity. - The right endpoint of \( K \) is \(6\) and it extends from negative infinity. Therefore, the union can be expressed as: \[ J \cup K = [-2, \infty) \cup (-\infty, 6) = (-\infty, 6) \cup [-2, \infty) \] Since \(-2\) is included in \( J \) and \( K \) extends to \(6\) but does not include it, we can express the union in interval notation as: \[ J \cup K = \{x \mid -2 \leq x < 6\} \] Thus, the correct answer is: \[ \{x \mid -2 \leq x < 6\} \]