false vs mistaken

false and mistaken both are adjectives.

Word	Noun	Adjective	Verb	Adverb
false	No	Yes	No	Yes
mistaken	No	Yes	No	No

As adjectives, false and mistaken are synonyms defined as:

false (adjective)	mistaken (adjective)
not in accordance with the fact or reality or actuality	arising from error
not genuine or real; being an imitation of the genuine article	wrong in e.g. opinion or judgment
adopted in order to deceive
designed to deceive
(used especially of persons) not dependable in devotion or affection; unfaithful
arising from error
inaccurate in pitch
deliberately deceptive
erroneous and usually accidental
inappropriate to reality or facts

false (adverb)	mistaken (adverb)
in a disloyal and faithless manner