Let's analyze each statement carefully:

1. The line that can be drawn through points C and D is contained in plane Y.

   • If both points C and D lie in plane Y, then the line passing through these two points will also lie in plane Y. This is true if the points are in the plane, but without explicit information about the positions of points C and D, we can't confirm this as true.

2. The line that can be drawn through points D and E is contained in plane Y.

   • If points D and E both lie in plane Y, then the line passing through them will also be in the plane. This statement would be true only if D and E are known to be in plane Y. Without more information, this statement cannot be guaranteed as true.

3. The only point that can lie in plane X is point F.

   • This statement seems restrictive because usually, planes contain an infinite number of points. Stating that only one point, F, lies in plane X is unusual unless this is a specific setup in a diagram. However, generally, planes have multiple points, so this is most likely false.

4. The only points that can lie in plane Y are points D and E.

   • Planes generally contain infinite points, not just two points. Saying that only D and E lie in plane Y contradicts the nature of a plane. Hence, this is false.

Conclusion:

• The truth of the first two statements depends on the positions of the points within the planes. However, generally speaking, the second statement ("The line that can be drawn through points D and E is contained in plane Y") is more likely to be true in common scenarios where points D and E lie in plane Y.

Would you like more details or have any other questions?

Related Questions:

1. What is the general definition of a plane in geometry?
2. How many points are required to define a plane?
3. How do we determine if a line is contained in a plane?
4. Can a plane exist with just one point?
5. How can we find the intersection of two planes?

Tip: To confirm whether a line lies in a plane, check if both points defining the line are in the plane.