The Antelope Valley district shall be governed by a district board consisting of seven members, as follows:
(a) Two members of the City Council of the City of Lancaster appointed by the city council.
(b) Two members of the City Council of the City of Palmdale appointed by the city council.
(c) Two persons appointed by the member of the Board of Supervisors of the County of Los Angeles who represents a majority of the population of the Antelope Valley district, one of whom may be that supervisor.
(d) A public member who shall be appointed by the members appointed pursuant to subdivisions (a) to (c), inclusive.