No searches based on probable cause are violations of Fourth Amendment rights.
Some warrantless searches are violations of Fourth Amendment rights.
Therefore, some warrantless searches are not searches based on probable cause.

Use the five rules to determine whether the following standard-form syllogisms are valid from the Boolean standpoint, valid from the Aristotelian standpoint, or invalid. For those that are invalid from either the Boolean or Aristotelian standpoint, name the fallacy or fallacies committed. Check your answer by constructing a Venn diagram for each.