Some basic properties of α-planes of type-2 fuzzy sets are investigated and discussed in connection with the similar properties of α-cuts of type-1 fuzzy sets. It is known, that standard intersection and standard union of type-1 fuzzy sets (it means intersection and union under minimum t-norm and maximum t-conorm, respectively) are the only cutworthy operations for type-1 fuzzy sets. Recently, a similar property was declared to be true also for α-planes of type-2 fuzzy sets in a few papers. Thus, we study under which t-norms and which \mbox{t-conorms} are intersection and union of the type-2 fuzzy sets preserved in the α-planes. Note that understanding of the term α-plane is somewhat confusing in recent type-2 fuzzy sets literature. We discuss this problem and show how it relates to obtained results.