Prove that any monotonic boolean function may be expressed with $\{\land, \lor, 1, 0\}$. Here under monotonic Boolean function is understood such boolean function $F$, that: $$\forall (x,y): x\leq y \longrightarrow F(x)\leq F(y)$$ ($x_j \leq y_j\ \forall j$ coordinates are being compared from left to right, in direct order)
Not sure, but it seems to me, that we may use here Disjunctive normal form of expression, but I've been trying to find any method to apply it with no effect so far..