(b) The county medical society of the county in which a county or part-county health district is established may submit to the board of supervisors a list of physicians from which the board of supervisors may choose the medical members of the board of health.
(c) The additional city representative members of the board of health shall each be appointed by the board of supervisors from a list of three persons submitted by the mayor or other administrative head of such city. Such city representative members so appointed shall have all the powers and duties conferred upon other members of said board.