Which of the following must be true? I. Any of two lines which are p

As there is a simple logic that governs parallel lines, we'll use it.
This is a Logical approach

I.
This is a basic definition of parallel lines and is true.

II.
This is also true for the same reason as above.
If we're not sure, we can try holding two sheets of paper above/below each other and SEE that this is true.
This is similar to drawing parallel lines on a sheet of paper to see that they must also be parallel.

III.
This is not true because a plane has infinitely many different directions.
For example, if you 'lift' the x-axis and y-axis 'up' above the xy plane they would still be parallel to it. (Formally, increase their 'z' value)
However, they are not parallel to each other.

(C) is our answer.