set about vs undertake

set about and undertake both are verbs.

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

As verbs, set about and undertake are synonyms defined as:

Other synonyms of set about include attempt.

set about (verb)	undertake (verb)
take the first step or steps in carrying out an action	promise to do or accomplish
enter upon an activity or enterprise	enter into a contractual arrangement
begin to deal with	enter upon an activity or enterprise
	accept as a charge
	accept as a challenge