disdainfulness vs arrogance

disdainfulness and arrogance both are nouns.

Word	Noun	Adjective	Verb	Adverb
disdainfulness	Yes	No	No	No
arrogance	Yes	No	No	No

As nouns, arrogance is a hypernym of disdainfulness; that is, arrogance is a word with a broader meaning than disdainfulness:

disdainfulness: the trait of displaying arrogance by patronizing those considered inferior
arrogance: overbearing pride evidenced by a superior manner toward inferiors

Other hypernyms of disdainfulness include haughtiness, hauteur, high-handedness, lordliness.

disdainfulness (noun)	arrogance (noun)
the trait of displaying arrogance by patronizing those considered inferior	overbearing pride evidenced by a superior manner toward inferiors