\( ( - 2,3 ) \cap [ - 1,4 ) = [ - 1,4 ) \)

To find the intersection of the intervals \( (-2, 3) \) and \( [-1, 4) \), we need to determine the set of points that are in both intervals. 1. **Interval \( (-2, 3) \)**: This interval includes all real numbers \( x \) such that \( -2 < x < 3 \). 2. **Interval \( [-1, 4) \)**: This interval includes all real numbers \( x \) such that \( -1 \leq x < 4 \). Now, let's find the intersection \( (-2, 3) \cap [-1, 4) \): - The lower bound of the intersection will be the maximum of the lower bounds of the two intervals. The lower bound of \( (-2, 3) \) is \(-2\) and the lower bound of \( [-1, 4) \) is \(-1\). The maximum of these two is \(-1\). - The upper bound of the intersection will be the minimum of the upper bounds of the two intervals. The upper bound of \( (-2, 3) \) is \(3\) and the upper bound of \( [-1, 4) \) is \(4\). The minimum of these two is \(3\). Thus, the intersection is: \[ [-1, 3) \] So, the statement \( ( - 2,3 ) \cap [ - 1,4 ) = [ - 1,4 ) \) is incorrect. The correct intersection is: \[ (-2, 3) \cap [-1, 4) = [-1, 3) \]