The trustees appointed in accordance with the foregoing provisions shall constitute a board of trustees for the mosquito abatement district for which they are appointed, and such board of trustees is declared to be the corporate authority of said district and shall exercise all of the powers and control all of the affairs and property of such district. Such board of trustees may provide and adopt a corporate seal. Immediately after their appointment and at their first meeting in December of each year thereafter the board of trustees shall elect one of their number as president, one as secretary, and one as treasurer, and shall elect such other officers as may be necessary. The board of trustees shall provide for the time and place of holding its regular meetings, and may establish rules for its proceedings. Special meetings may be called by the president of the board or by any three trustees, but each member of the board shall be given notice of such special meeting at least three hours prior thereto. All of the meetings of such board, whether regular or special, shall be open to the public. A majority of the board of trustees shall constitute a quorum but a smaller number may adjourn from day to day. Said board shall keep a regular book of records of all of the proceedings of said board, which book shall be open to the inspection of any person residing in said district at all reasonable and proper times.