So 몰라요 is what negates this sentence?
Yes, since in English there is no word for "to not know".
Its's not really negating per se. 몰라다 is the verb: to not know. I suppose you could say 안 몰라요 to say "i don't not know" = I do know.
No, it is 모르다. Since the stem ends in 르, it is dropped and turns to 몰ㄹ. Since the last vowel is ㅗ, ㅏ is used and the final form is 몰라요.
Is there a verb "to know"?
So it's basically like French: 'Cette femme ignore ce livre'.
Can't I use 알지 않아요?
Its technically valid Korean, but typically you would use the antonym if its available: 모르다.
"You don't know men" really helped here!!
So 모르지 않아요 wouldn't work? Can anyone please explain why?
모르다 is "to not know". So its long form negation 모르지 않다 would convey "to know". Its technically valid Korean, but typically you would use the antonym if its available: 알다.