Which of the following is correct:

a$)$ Union density is higher in the public sector than the private sector.

b$)$ There are more female union members in the private sector than in the public sector.

c$)$ Union density in the public sector has been declining since $1984.$

d$)$ There are more professional employees unionized in the private sector than in the public sector.

e$)$ Union density in the public sector cannot increase in the future.