The scope of logic

Which of the following arguments is valid? Which is invalid?

1. • Socrates is a man.

   • All men are carrots.

   • Socrates is a carrot.

2. • Abe Lincoln was either born in Illinois or he was once president.

   • Abe Lincoln was never president.

   • Abe Lincoln was born in Illinois.

3. • If I pull the trigger, Abe Lincoln will die.

   • I do not pull the trigger.

   • Abe Lincoln will not die.

4. • Abe Lincoln…

Could there be:

1. A valid argument that has one false premise and one true premise?

2. A valid argument that has only false premises?

3. A valid argument with only false premises and a false conclusion?

4. An invalid argument that can be made valid by the addition of a new premise?

5. A valid argument that can be made invalid by the addition of a new premise?

In each case: if so, give an example; if…