prove that {$↔,⊕$} is incomplete set?
The universal method to check whether a set of connectives is complete in this sense is Post's classes: there are 5 function classes such that a set of functions is complete iff it isn't a subset of any of these 5. One of the 5 is affine functions, as described in Yuval's answer; the rest are monotone, self-dual, 0-preserving, and 1-preserving functions. 

It's pretty easy to show that all 5 classes are closed: any composition of functions from one of them will also belong to the same class. So if your set is a subset of a Post's class, it can't be complete. Showing the other direction is more complicated, but likely you'll learn the proof in the near future.