1. Some politicians are people who will stop at nothing to win an election, and no people who will stop at nothing to win an election are true statesmen. Hence, no politicians are true statesmen.
2. All meticulously constructed timepieces are true works of art, for all Swiss watches are true works of art and all Swiss watches are meticulously constructed timepieces.
Use the counterexample method to prove the following categorical syllogisms invalid. In doing so, follow the suggestions given in the text.