Database

[{name:"Peter",city:"New York",dogs_owned:2,cats_owned:1,},{name:"Amir",city:"Chicago"},{name:"James",city:"Chicago",dogs_owned:3},{name:"Leilani",city:"Chicago",cats_owned:3}]

Query

db.collection.find({city:"Chicago",$or:[{dogs_owned:{$exists:true}},{cats_owned:{$exists:true}}]})

Result