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It is indeed safe to add apple cider vinegar to your cat's water. Many sources claim that is has multiple health benefits. I don't know how true all of them are, but I do know that it isn't going to hurt anything to try it. You can try adding about 1 teaspoon per day to your cat's water. I would give fresh water everyday, and add the vinegar to it. Here is a link to a page with some more information about this:
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No, the apple cider vinegar itself mixed in the water will not cause dehydration. The only way you would have this problem is if your cat won't drink the water because they don't like the taste. If you want an alternative way to give it to your cat, you could try mixing it in a little canned cat food once a day.