Final Answer:
Lines s and t do not intersect in a point, so they do not determine a plane. This is B) Not valid
Step-by-step explanation:
Lines s and t not intersecting in a point does not imply that they do not determine a plane. In Euclidean geometry, two distinct lines always determine a unique plane. The intersection of lines s and t could be at infinity or may not exist within a defined region, but they still determine a plane. The condition for lines to determine a unique plane is that they must not be parallel. Therefore, the assertion that lines s and t do not determine a plane solely based on the fact that they don't intersect in a point is not valid.
In geometry, when two lines don't intersect, there are two possibilities: they are either parallel or they are skew lines. Parallel lines lie in the same plane, and hence, they do determine a plane. Skew lines, on the other hand, do not lie in the same plane but still determine a unique pair of planes. Therefore, the claim in the question oversimplifies the geometric relationship between lines and planes. To establish whether lines s and t determine a plane, it is essential to consider factors like parallelism or skewness, rather than just their intersection point.
In conclusion, the statement that lines s and t do not determine a plane based on their lack of intersection in a point is not valid. The determination of a plane is contingent on factors beyond a single intersection point, and in the realm of Euclidean geometry, two non-parallel lines always uniquely determine a plane.