Final answer:
An easement by prescription may be established if there is open, notorious, and continuous use of property without the owner's knowledge, yet whether the neighbor's claim will be successful depends on specific jurisdictional law.
Step-by-step explanation:
The question revolves around whether or not a neighbor's act of planting a rose garden on someone else's property without their knowledge can lead to an easement by prescription. Generally, for an easement by prescription to be established, there must be open, notorious, continuous, and hostile use of the property for a certain statutory period. The owner's lack of knowledge due to being housebound doesn't necessarily preclude the establishment of an easement, as the law doesn't always require that the owner has actual knowledge of the use. However, the exact claim would depend on the law in the jurisdiction, including the specifics of proving such a claim.
Considering the provided options, if the neighbor's use of the property was open and notorious, a claim for an easement by prescription may succeed under the theory that knowledge of the use is not necessary (Option A). However, if the law in the jurisdiction requires some form of notice or an opportunity for the owner to object, then the claim may fail (Option D).