Question

error analysis in exercises 19 and 20, describe and correct the error in the conditional statement about lines. 19. if two lines do not intersect, then they are parallel. 20. if there is a line and a point not on the line, then there is exactly one line through the point that intersects the given line.

Explanation:

1. For exercise 19, the error is that the statement is not true in 3 - D space. In 3 - D, non - intersecting lines can be skew. To be parallel, two lines must be in the same plane and not intersect.
2. For exercise 20, there are infinitely many lines through a point not on a given line that can intersect the given line.

Answer:

1. The error is that the statement is only true in 2 - D. In 3 - D, non - intersecting lines may be skew. A corrected statement could be: If two lines are in the same plane and do not intersect, then they are parallel.
2. The error is that there are infinitely many lines through the point that can intersect the given line. A corrected statement could be: If there is a line and a point not on the line, then there are infinitely many lines through the point that intersect the given line.