Section 1. Except as otherwise provided by law, city councils shall have the powers of towns; boards of aldermen shall have the powers, perform the duties and be subject to the liabilities of selectmen, except with respect to appointments, and the mayor shall have the powers, perform the duties and be subject to the liabilities of selectmen with respect to appointments, but all his appointments shall be subject to confirmation and rejection by the aldermen, and upon the rejection of a person so appointed the mayor shall within one month thereafter make another appointment. In cities having a single legislative board other than a board of aldermen, such board shall, so far as appropriate and not inconsistent with the express provisions of any general or special law, have the powers, perform the duties and be subject to the liabilities of the board of aldermen.