Final answer:
The given statement, "In 3D space, two lines parallel to a plane are parallel," is false (F) because in 3D space, two lines parallel to a plane are not necessarily parallel to each other.
Step-by-step explanation:
When a line is parallel to a plane, it means the line doesn’t intersect the plane. However, two lines can be parallel to the same plane yet have different inclinations in space, resulting in them never intersecting each other, hence being parallel to the plane but not to each other. Think of railroad tracks: they are parallel to the ground (plane) but never meet each other, maintaining their distinct parallel paths.
In spatial geometry, it’s crucial to understand that parallelism with a plane doesn’t imply parallelism between lines in 3D space. Even if both lines never touch the plane, their directional paths can differ, leading to non-intersecting lines that aren't parallel to each other. Therefore, in 3D space, two lines parallel to a plane are not necessarily parallel to each other.
Correct answer: False (F)