Search online for beware of dog lawsuits in the US as an example of liability. The problem is that these laws vary by jurisdiction, so for example in California those signs do not protect the homeowner if someone is bitten on their land [1]. Michigan State University has a comprehensive overview of dog bite laws in the US indicating where "beware of dog" signs legally protect the owner from lawsuits [2] when someone trespasses.
To be clear though: No matter the interaction between postings and liability, successfully excluding people does protect you because it prevents the injury in the first place.
[1]: https://www.enjuris.com/california/premises-liability/beware...
[2]: https://www.animallaw.info/topic/table-dog-bite-strict-liabi...