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Are all cities filthy and disgusting places filled with slums, homeless people, and high rates of crime?

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The question, as posed, is a problem of propositional logic.

In its most general sense, a city is any large human settlement. More specifically, jurisdictions define cities in relation to certain characteristics, such as population or incorporation status. They are larger than a town or a village.

The question contains four separate inquiries, and the construction of the question requires all four criteria to be met in order for the response to be "yes." These are:

  1. Do all cities have homeless people?
  2. Are all cities filled with slums?
  3. Do all cities have high rates of crime?
  4. Are all cities filthy and disgusting?

Sierra Madre, California, is a city as defined in the California Government Code. According to the most recent homeless census in that city, it has no homeless people living in it. Therefore, not all cities have homeless people. Because we can prove that not all cities have homeless people we can, logically, also establish that the response to the question "Are all cities filthy and disgusting places filled with slums, homeless people, and high rates of crime?" is no.

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