Some nebulas are clouds of gas.
Some clouds of gas are objects invisible to the naked eye.
Therefore, some objects invisible to the naked eye are nebulas.

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.