Final answer:
The use of a Venn diagram shows that the statement is a valid deductive inference, as the premise 'No summer romances are banal pastimes' supports the conclusion, meaning there is no fallacy. The statement is therefore valid and not a Boolean or Aristotelian fallacy.
Step-by-step explanation:
The statement 'No summer romances are banal pastimes. Therefore, it is false that some summer romances are banal pastimes' can be evaluated using Venn diagrams to determine its validity. Since the premise 'No summer romances are banal pastimes' can be translated to mean there is no overlap between the set of 'summer romances' and 'banal pastimes' in a Venn diagram, the conclusion 'it is false that some summer romances are banal pastimes' is supported by the premise. This forms a valid deductive inference, as the truth of the premise guarantees the truth of the conclusion. However, given that there are no fallacies involved in this reasoning, neither Boolean nor Aristotelian, the correct answer is that the statement is valid without any fallacy present.