Members of the State Duma formed factions in such a way that for any two fractions $A $ and $B$ (not necessarily different), $\overline{A \cup B}$ is also faction ($\overline{C}$ denotes the set of all members of the Duma, not including in $C$). Prove that for any two factions $A$ and $B$, $A \cup B$ is also a faction.