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I am co nfused with these true and false questions. Any help would be appreciated.

Enter T or F depending on whether the statement is true or false. (You must enter T or F -- True and False will not work.) All planes and lines are assumed to be in (Real number)^3 .

1. Two lines parallel to a third line are parallel.
2. Two lines perpendicular to a third line are parallel.
3. Two lines parallel to a plane are parallel.
4. Two planes parallel to a line are parallel.
5. Two planes parallel to a third plane are parallel.
6. Two planes either intersect or are parallel.
7. Two lines either intersect or are parallel.
8. Two lines perpendicular to a plane are parallel
9. Two planes perpendicular to a line are parallel.
10. Two planes perpendicular to a third plane are parallel.

Answer
I'll try to fill these out and give explanations as needed.

1. T

2. F ; think of the familiar x,y,z axes

3. F ; just imagine the 2 lines as being in the plane and thus parallel to the plane (i.e., distance to plane for all points in line are equal, namely 0); 2 lines in a plane are not necessarily parallel to each other

4. F

5. T

6. T

7. F ; not in R3

8. T

9. T

10. F ; take 2 planes intersecting in a line at some arbitrary angle, they are not parallel to each other but are perpindicular to the plane perpindicular to the intersecting line.  

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