[{"_id":"positive1","arr":[["option1","option2"],["option3","option4"]]},{"_id":"positive2","arr":[["option1","option2"],["option1","option2","option3","option4"]]},{"_id":"negative1","arr":[["option1","option2"]]},{"_id":"negative2","arr":[["option1","option2"],["option3"]]}]

db.collection.find({"$expr":{"$anyElementTrue":{"$map":{"input":"$arr","as":"a","in":{"$setIsSubset":[/** your input here*/["option3","option4"],"$$a"]}}}}})