"Either your dog or your cat eats" vs. "Either your dog or cat eats"
Version (1) seems correct to me, but I cannot explain why it is correct grammatically. Could someone explain please?
- Either your dog or your cat eats my garbage.
- Either your dog or cat eats my garbage.
Solution 1:
It's not a question of correctness. Most speakers would "delete" the second your in most contexts, but if they specifically wanted to pin the blame on the addressee's pets (rather than another neighbour's pets, for example), they'd probably repeat the pronoun for the sake of emphasis.
Solution 2:
This is another example of the common syntactic process called Conjunction Reduction, which gets rid of repeated material in parallel clauses or phrases. It's optional, so you can do it or not do it, as you like.
There's no difference in meaning, because syntactic processes don't generally affect meaning, but rather structure. The usual purpose of conjunction reduction is to shorten the spoken sentence.
That's all. In writing, it usually produces ambiguity, and in the wrong hands, occasionally ungrammaticality; in writing one shouldn't delete words without a good reason.
Written language needs all the help it can get to represent spoken language.