Simple Conceptual Question Regarding Pascal's Principle

[zak.hja]

Homework Statement

There's a conceptual question I've encountered in my reading, wherein we're supposed to determine the validity of a statement: "According to Pascal’s principle, if you increase the pressure enough so that the force at one end of an oil-filled tube increases by 10 N, the force will increase at all points in the tube by 10 N". The thing that's really bothering me is that this statement is supposedly true.

Homework Equations

P=F/A

The Attempt at a Solution

I know that Pascal's principle pertains to the applied pressure at any point within an enclosed fluid; the applied pressure is transmitted undiminished, throughout. It isn't necessarily true to say the force is the same, is it? As such, I find the statement to be highly problematic.
Or, does the fact that it's an oil-filled "tube" imply that the area is uniform throughout. Even then, is it correct to say the force increases at all points by 10N?

Many thanks!

 

[SteamKing]

If you assume, instead, that this statement is not true, does that resolve your doubts? That is, does assuming the statement not to be true line up with what you understand to be Pascal's Principle? Is pressure the same as force?