interior design vs liberal arts

interior design and liberal arts both are nouns.

Word	Noun	Adjective	Verb	Adverb
interior design	Yes	No	No	No
liberal arts	Yes	No	No	No

As nouns, liberal arts is a hypernym of interior design; that is, liberal arts is a word with a broader meaning than interior design:

interior design: the art of designing the interior decoration for a house, office, or other architectural space
liberal arts: studies intended to provide general knowledge and intellectual skills (rather than occupational or professional skills)

Other hypernyms of interior design include arts, humanistic discipline, humanities.

interior design (noun)	liberal arts (noun)
the art of designing the interior decoration for a house, office, or other architectural space	studies intended to provide general knowledge and intellectual skills (rather than occupational or professional skills)