Given three sets: $X, Y, Z$ and the two set operations: union and intersection. What is the maximum length of a 'formula' which is not reducible to a shorter formula.
Eg. the formula $(X \cap Y) \cup X$ can be reduced to the formula $X$.
However the formula $Y \cap(X \cup Z)$ is not reducible in length.
I've been thinking about this problem for a while now, but can't seem to get past a length of 3. (the length being the amount of set symbols).