plunge vs set about

plunge is a noun but set about is not a noun.

Word	Noun	Adjective	Verb	Adverb
plunge	Yes	No	Yes	No
set about	No	No	Yes	No

As verbs, set about is a hypernym of plunge; that is, set about is a word with a broader meaning than plunge:

Other hypernyms of plunge include begin, commence, get, get down, set out, start, start out.

plunge (noun)	set about (noun)
a brief swim in water
a steep and rapid fall

plunge (verb)	set about (verb)
begin with vigor	take the first step or steps in carrying out an action
devote (oneself) fully to	enter upon an activity or enterprise
cause to be immersed	begin to deal with
immerse briefly into a liquid so as to wet, coat, or saturate
thrust or throw into
fall abruptly
drop steeply
dash violently or with great speed or impetuosity