Well to start with in most situations you won't need the "be" in "liable to" or "prone to" and "apt" usually isn't attached to either. If someone is "liable to" do something, it means there is a high chance they will do it or it is a very believable possibility. Example: "Jimmy is liable to skip work." This would make sense if Jimmy had a history of missing work or an event happened that day that would cause him to skip work. If someone is "prone to" something, it means that the thing they are prone to happens often or happens to them easily. Example: "Jimmy is prone to sudden illness." This would make sense if Jimmy was often suddenly sick, or Jimmy easily becomes sick. "Apt" has two meanings that you could be getting at. It could mean "appropriate or suitable in the circumstances" Example: "An apt decision" would be a decision that is appropriate or suitable in the circumstances of the situation. "The boss's decision to fire Jimmy was apt considering how prone he is to skipping work." The second meaning of apt is "having a tendency to do something," so a similar meaning to saying someone is "liable to" something. Example: "Jimmy was apt to forget to set his alarm." However it is worth noting that you rarely hear this usage, and as a native speaker it sounds weird to me and I would rather use a different word. I hope this helps you! ^_^