cow pen vs pen

cow pen and pen both are nouns.

Word	Noun	Adjective	Verb	Adverb
cow pen	Yes	No	No	No
pen	Yes	No	Yes	No

As nouns, pen is a hypernym of cow pen; that is, pen is a word with a broader meaning than cow pen:

cow pen (noun)	pen (noun)
a pen for cattle	female swan
	a writing implement with a point from which ink flows
	an enclosure for confining livestock
	a correctional institution for those convicted of major crimes
	a portable enclosure in which babies may be left to play

cow pen (verb)	pen (verb)
	produce a literary work