Reduction — Do they work for unrelated problems?
If you have a problem $X$ that is in P, then you can construct a polynomial time reduction to any problem $Y$ in NP (or in 'any' other class of problems*). This is possible, as our 'reduction' is allowed to spend polynomial time on the input of $X$, so it can simply determine whether a given input $I$ for $X$ is a 'yes'-input in polynomial time and map to a trivial input for $Y$ with the same truth-value.



*: To be precise, any decision problem such that we can find at least one 'yes'-instance and one 'no'-instance, which holds for pretty much any interesting decision problem.