Which statement is FALSE?The lieutenant governor becomes governor if the office becomes vacant. The plural executive is composed of appointed...

This depends on what government we are talking about -
either a national or state government - but I will do my best to
answer.

A. This is certainly true in all US states that I
am aware of.

B. This is FALSE, at least in Texas. See the
following link:
http://www.cathedral-elpaso.org/advancedstudies/govt2306/ch02/sl-ch02-trms.htm

C.
This seems true in all US states that I am aware of.

D.
This is certainly true in all US states that I am aware
of.

E. This is certainly true in all US states that I am
aware of.

To answer your question, the false statement
seems to be B: The plural executive is composed of appointed
officials.