Partial Solutions for Categorical Argument Exercises Using Immediate Inferences

Use immediate inferences and Venn diagrams to determine which of the following are valid.

1.		All P are nonM.	==== Obversion ==>	No P are M.
		Some S are nonM.	==== Obversion ==>	Some S are not M.
		Some S are P.	==============>	Some S are P.
2.		No nonP are M.	==== Conversion ==>	No M are nonP.	==== Obversion ===>	All M are P.
		No S are nonM.	==== Obversion ====	================	===============>	All S are M.
		All S are P.	================	================	===============>	All S are P.
3.		Some P are nonM.	==== Obversion ====	================	===============>	Some P are not M.
		No nonM are S.	==== Obversion ===>	All nonM are nonS.	== Contraposition ==>	All S are M.
		Some S are P.	================	================	===============>	Some S are P.
4.		All M are nonP.	==== Obversion ==>	No M are P.
		Some M are nonS.	==== Obversion ==>	Some M are not S.
		Some S are P.	==============>	Some S are P.
5.		All nonP are nonM.	== Contraposition =>	All M are P.
		All nonM are nonS.	== Contraposition =>	All S are M.
		All S are P.	==============>	All S are P.
6.		No nonM are P.	==== Conversion ==>	No P are nonM.	==== Obversion ===>	All P are M.
		No nonS are M.	==== Conversion ==>	No M are nonS.	==== Obversion ===>	All M are S.
		No S are P.	================	================	===============>	No S are P.
7.		All nonM are P.	The easiest thing to do here is use nonM as the middle term!
		All S are nonM.	Or: Use obversion on the second premise (nonM will remain in the first premise).
		All S are P.
8.		Some nonM are P.	==== Conversion ==>	Some P are nonM.	==== Obversion ===>	Some P are not M.
		All nonM are nonS.	=== Contraposition ==	================	===============>	All S are M.
		Some S are not P.	================	================	===============>	Some S are not P.