1. Examine each of the following syllogisms and determine if the validity of the conclusion can be necessarily deduced from the premises. (In other words, is the syllogism valid or invalid?)
Some students are not clever.
All freshmen are students.
Therefore, some freshmen are not clever.
No Christian worships idols.
Some pagans worship idols.
Therefore, some pagans are not Christians.
Some experts are highly paid.
No teachers are highly paid.
Therefore, some teachers are not experts.
All teachers are poor and overworked.
Some women are teachers.
All women are poor and overworked.
All tricks are dishonest.
All card players win tricks.
Therefore, all card players are dishonest.
No flower is a mineral.
Every flower is a substance.
Therefore, no mineral is a flower.
2. Consider the following propositions as conclusions to a syllogism. Find two premises that together will necessarily prove the validity of these conclusions.
a. No fish is a mammal.
b. Not every genius is a mathematician.
c. No circle is a square.