The Categorical Syllogism
Logic Exercises

Indicate a) whether the following arguments are valid or invalid by checking the appropriate square.  Also, if the syllogism is invalid indicate which rule of logic was violated. 
To make this easier, use the following steps:
Step 1:  Circle the middle term.
Step 2:  Determine what kind of statement (i.e., A, I, E, or O) is the first premise.  Then do the same for the second premise.  Finally, determine what kind of statement is the conclusion. 
Step 3:  Highlight all the distributed terms using a colored highlighter. 
Step 4:  Check to see if the middle term is distributed at least once.  If it is not, no need to proceed further, the syllogism is invalid.
Step 5:   If there are any distributed terms in the conclusion, check to see if those very terms are distributed in the premises. 
Step 6:  Check the rest of the rules.  If no rules are violated, the syllogism is valid. 

1.
All C is P.
J is P.
Ergo, J is C.
Valid [ ] Invalid [ ]
Reason for Invalidity:

2.
Some Lifeissues.net readers are philosophers.
Sean is a philosopher.
Ergo, Sean is a Lifeissues.net reader.
Valid [ ] Invalid [ ]
Reason:

3.
No man is perfect
Some men are presidents.
Ergo, some presidents are not perfect.
Valid [ ] Invalid [ ]
Reason:

4.
All matter obeys wave equations.
All waves obey wave equations.
Ergo, all matter is waves.
Valid [ ] Invalid [ ]
Reason:

5.
All human action is conditioned by circumstances.
All human action involves morality.
Ergo, all that involves morality is conditioned by circumstances (moral relativism).
Valid [ ] Invalid [ ]
Reason:
 
6.
All that is good is pleasant.
All eating is pleasant.
Ergo, all eating is good.
Valid [ ] Invalid [ ]
Reason

7.
All patriots are voters.
Some citizens are not voters.
Ergo, some citizens are not patriots.
Valid [ ] Invalid [ ]
Reason:

8.
All potatoes have eyes.
Frank's head has eyes.
Ergo, Frank is a potato head.
Valid [ ] Invalid [ ]
Reason:

9.
All A are B
Some C are not B.
Ergo, some C are not A.
Valid [ ] Invalid [ ]
Reason:

10.
All a priori categories are conditions for the possibility of knowing anything.
Some a posteriori imperatives of an a-cosmic ethics are not conditions for the possibility of knowing anything.
Ergo, some a posteriori imperatives of an a-cosmic ethics are not a priori categories.
Valid [ ] Invalid [ ]
Reason:

11.
No oak trees bear fruit.
No maple trees bear fruit.
Therefore, no oak trees are maples.
Valid [ ] Invalid [ ]
Reason:

12.
All socialists favor higher taxes.   
Some Liberals favor higher taxes.   
Ergo, some Liberals are Socialists.
Valid [ ] Invalid [ ]
Reason:

13.
All educated people have worked hard.
Some students are not educated.
Ergo, some students have not worked hard.
Valid [ ] Invalid [ ]
Reason:

14.
Mathematicians know what mathematics is.
No philosopher is a mathematician.
Ergo, no philosopher knows what mathematics is.
Valid [ ] Invalid [ ]
Reason:

15.
All scientific knowledge is a work of reason.
All scientific knowledge is true.
Ergo, all that is true is a work of reason.
Valid [ ] Invalid [ ]
Reason:

16.
All married people know about marriage problems.
No priests are married people.
Ergo, no priests know about marriage problems.
Valid [ ] Invalid [ ]
Reason:

17.
All C are B
All T are B
Ergo, all T are C
Valid [ ] Invalid [ ]
Reason:

18.
All chickens are born from eggs.
All turkeys are born from eggs.
Ergo, all turkeys are chickens.
Valid [ ] Invalid [ ]
Reason:

19.
Nothing easy is worthwhile.
Nothing good is easy.
Ergo, nothing good is worthwhile.
Valid [ ] Invalid [ ]
Reason:

20.
All contraceptives acts are for avoiding pregnancy.
All use of NFP is for avoiding pregnancy.
Ergo, All use of NFP is contraceptive.
Valid [ ] Invalid [ ]
Reason:

21.
All Germans despise Judaism.
All of the people reading this text are German.
Ergo, all of the people reading this text despise Judaism.
Valid [ ] Invalid [ ]
Reason:

22.
All parts of a living organism are inside the body.
The fetus is inside the (mother's) body.
Therefore, the fetus is a part of the living organism (mother's body)
Valid [ ] Invalid [ ]
Reason:


ANSWERS