  Given two testable properties $\mathcal{P}_{1}$ and $\mathcal{P}_{2}$, under
what conditions are the union, intersection or set-difference of these two
properties also testable? We initiate a systematic study of these basic
set-theoretic operations in the context of property testing. As an application,
we give a conceptually different proof that linearity is testable, albeit with
much worse query complexity. Furthermore, for the problem of testing
disjunction of linear functions, which was previously known to be one-sided
testable with a super-polynomial query complexity, we give an improved analysis
and show it has query complexity $O(1/\eps^2)$, where $\eps$ is the distance
parameter.
