A very quick and safe way to check if a domain is in use is to query for NS records (e.g. $dig ycombinator.com NS). This will give some false positives though.
Sorry to sound pedantic, Im just trying to make sure I understand correctly. A false positive would be domain doesn't exist but it has NS records, and a false negative would be does exist but doesn't have MX records. Is that right?
Positive for me would be that a domain is free, so a false positive is a domain that seems to be free (no NS record) but is in fact taken (because it is registered but nothing has been added to the DNS). But you're right, my wording wasn't precise.