Yes and No

I was teaching my partner some mandarin recently and I came to the conclusion that "yes" and "no" are very weird constructs of language. We were practicing one day, where I'd ask her questions in English and she'd reply in Mandarin. I asked her a yes/no question and she replied 不, to which I surprised myself by pointing out that 不 is ever only used in a negatory manner. People who know some Mandarin would interject and say, but there is 不(bù), 没(méi), and 无(wú) that can be used in stead of "no". Yes, they can, but they're usually not used without context. Let's look at some concrete examples to understand.