undertake vs set about

undertake and set about both are verbs.

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

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

Other synonyms of undertake include attempt.

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