A person is not qualified for membership in the legislature who is disqualified to hold public office under the provisions of art. XII, § 4, Constitution of the State of Alaska, and as it may be implemented by law. Each member of the legislature, before entering upon the duties of the office, shall take the oath of office prescribed in art. XII, § 5, Constitution of the State of Alaska, and such further oath or affirmation prescribed by law for members of the legislature or other officers of the state.