Exercise
For each syllogism below, rewrite its statements in standard form and then give its figure and mood (e.g., "first figure, mood AAA" or its name, e.g., Barbara). Next, using the Venn diagram method, prove that the syllogism's form is valid or invalid. Show the resulting graph and if the form is not valid, explain why in reference to the Venn diagram you have constructed.
1. Not a single Republican is an advocate of socialized medicine. And yet, everyone in favor of smaller government is also a Republican. I think that it follows, and you will agree, that no one in favor of small government is a supporter of socialized medicine.
2. Everybody who knows their subject well turns out to be a good teacher. A few of those who know their subject well are scientists. So it follows that only some scientists are good teachers.
3. Some of the politicians I have encountered are not excellent musicians. At the same time, every barber I have met has been an excellent musician. So, it follows that some of the politicians I have met over the years are clearly not barbers.