Is it legal to kill cats/dogs that come onto your property?

Question Details: My parents want to leave me their house when they retire. However, they have a huge problem with neighborhood cats coming into the yard and pooping all over the place, eating all the fish in their little fishpond area and causing all sorts of other property damage. Don't get me wrong, I'm not a cat hater. I've owned 2 and I'm a destruction hater. I've looked online for this answer, but to no avail. Almost every response seems to be, "Go ask your local animal police". Yet, the police are incompetent so I'd like to know what I'm "allowed" to do on my own? Every time I google this question, I drown in an ocean of irrelevant pet laws, so I'd like to ask it here in a series of short, easy, QA's. Are you legally entitled to the following: cage/trap/euthanize wandering cats/dogs on your property; cage/trap/euthanize cats/dogs defecating on your property; or cage/trap/euthanize cats/dogs causing destruction of property and for each question I'm looking for 2 answers, 1 for collared identifiable pets and 1 for collarless "strays". In many of the forums I read, people give alternative solutions instead of just answering the question at hand, so let me get all of that out of the way right now. No, I won't buy a dog, I won't defer to another person/group to fix my problem for me, I won't waste time or money using sprays or other deterrents and I won't pay money to have a shelter take them.

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