dunce cap vs hat

dunce cap and hat both are nouns.

Word	Noun	Adjective	Verb	Adverb
dunce cap	Yes	No	No	No
hat	Yes	No	Yes	No

As nouns, hat is a hypernym of dunce cap; that is, hat is a word with a broader meaning than dunce cap:

dunce cap: a cone-shaped paper hat formerly placed on the head of slow or lazy pupils
hat: headdress that protects the head from bad weather; has shaped crown and usually a brim

Other hypernyms of dunce cap include chapeau, lid.

dunce cap (noun)	hat (noun)
a cone-shaped paper hat formerly placed on the head of slow or lazy pupils	an informal term for a person's role
	headdress that protects the head from bad weather; has shaped crown and usually a brim

dunce cap (verb)	hat (verb)
	put on or wear a hat
	furnish with a hat