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住んでいるのが好きです is a fragment of a sentence that is incorrectly constructed - the correct way to say "I like living in [place] would be 住むのが好きです. But why is this? In the present tense, the usual way to say "I live in [place]" is to use the state-of-being 〜ている, e.g., 私は日本に住んでいます。By that logic, "I lik...