Are 1. and 2. grammatical?
Yes, but (1) is a phrase not a full sentence (= "The crime that the city wants wiped out").
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Yes, but (1) is a phrase not a full sentence (= "The crime that the city wants wiped out").
To comment further on this, the three sentences are grammatical, but they would not be said in real life. When a city talks about crime, it's typically in the statement: "The city wants crime wiped out." That is, it's never "the crime," in this context. The reason for this is apparently that by saying "crime" this makes the city sound grand, like they're dedicated to wiping out all crime