# Logic Help

1. May 9, 2005

### kennethj67

I was looking to see if someone will be able to help me with the following pertaining to logic. I am having the toughest time right now and need assistance. Thank you for any help that you may supply.

1. Identify the subject and predicate terms in, and name the form of, each of the following propositions:

a. No athletes who have ever accepted pay for participating in sports are amateurs.

2. Name the quality and quantity of each of the following propositions, and state whether their subject and predicate terms are distributed or undistributed:

a. All those who died in Nazi concentration camps were victims of a cruel and irrational tyranny.

3. State the converses of the following propositions, and indicate which of them are equivalent to the given propositions:

a. All graduates of West Point are commissioned officers in the U.S. Army.

4. State the obverses of the following proposition:

a. No organic compounds are metal.

5. State the contrapositives of the following proposition and indicate which of them are equivalent to the given proposition:

a. Some soldiers are not officers.

6. What can be inferred about the truth or falsehood of the remaining propositions in each of the following sets (1) if we assume the first to be true, and (2) if we assume the first to be false?

a. No animals with horns are carnivores
b. Some animals with horns are carnivores
c. Some animals with horns are not carnivores
d. All animals with horns are carnivores

7. If “All socialists are pacifists: is true, what may be inferred about the truth or falsehood of the following proposition? That is, which could be known to be true, which known to be false, and which could be undetermined?

a. No socialists are nonpacifists.

2. May 9, 2005

### HallsofIvy

Staff Emeritus
You will have to give us some information as to what you know and what you can do.
What are the definitions of "subject" and "predicate" and what are the possible "forms"?

3. May 9, 2005

### kennethj67

To tell you the truth, I am just lost. Subject and predicate propositions are the traditional categorical propositions, identified as universal affirmative (A), universal negative (E), Particular affirmative (I), and Particular negative (O).

4. May 9, 2005

### honestrosewater

Welcome to PF! I'm glad you showed up :)
So what form is this?
Universal Affirmative A: All S are P
Universal Negative E: No S are P
Particular Affirmative I: Some S are P
Particular Negative O: Some S are not P

5. May 9, 2005

### kennethj67

Clueless, but I'm thinking particular negative

6. May 9, 2005

### honestrosewater

Underline the classes:
No athletes who have ever accepted pay for participating in sports are amateurs.
Replace the underlined parts with a letter, say S for athletes who have ever accepted pay for participating in sports and A for amateurs:
No S are A
Now just compare it to the four forms.

7. May 9, 2005

### kennethj67

ok, so this would be a universal negative then.

8. May 9, 2005

### honestrosewater

Right. Now the subject and predicate terms are the underlined parts. The subject term appears first; The predicate term appears second.

What form is this? What are the subject and predicate terms?
A term is distributed in a propostion if that proposition tells you something about all members of the class denoted by that term. Does this proposition tell you something about all members of the class denoted by the subject term? What about the predicate term?

9. May 9, 2005

### kennethj67

All those who died in Nazi concentration camps tells me something about all members. The predicate (I think) would be, "victims of a cruel and irrational tyranny.
Quantity would be universal
Quality would be affirmative
Subject term is distributed
Predicate term is distributed

10. May 9, 2005

### honestrosewater

You're right, except that the predicate term is undistributed.
All those who died in Nazi concentration camps were victims of a cruel and irrational tyranny.
What does this tell you about every member of the victims of a cruel and irrational tyrrany? Nothing- it only tells you that some of its members are those who died in Nazi concentration camps.
Can you figure out the forms of the propositions in 3, 4, and 5?

11. May 9, 2005

### kennethj67

I will have to work on those and get back with you. I appreciate the assistance.

12. May 9, 2005

### kennethj67

Here is what I came up with so far.
#3: Some comissioned officers in the U.S. Army are graduates of West Point.
#4: All organic compounds are metal
#5: Some nonofficers are not non-soldiers. Equivalent.
#6: If we assume that (a) is true, then;
(b) which is its contradictory, is false
(c) which is its subaltern, is true
(d) which is its contrary, is false
If we assume that (a) is false, then;
(b) which is its contradictory, is true
(c) which is its subaltern, is undetermined
(d) which is its contrary, is undetermined
#7: False

13. May 9, 2005

### honestrosewater

Correct, but note that this is a conversion by limitation, i.e., you are using subalternation, so you're assuming the subject class has at least one member. If you don't know what I'm talking about, nevermind- but if you are covering this, it's important to note it. Conversion by limitation is a valid inference, so this is equivalent.
Half correct. You forgot to replace the original predicate with its compliment.
Obversion steps:
1) No S are P
2) No S are non-P (replace predicate P with its compliment, non-P)
3) All S are non-P (reverse the quality- "All" to "No", "No" to "All")
Great job- all correct!

14. May 9, 2005

### kennethj67

So for question 4, would it be:
All organic compounds are non-metal

15. May 9, 2005

### kennethj67

Also, I wanted to know if I got the following correct.

A. Express each of the following propositions as equations or inequalities, representing each class by the first letter of the English term designating it, and symbolizing the proposition by means of a Venn diagram:

1. All merchants are speculators. Answer: MS=0 (with bar over the "S")
2. Some stockholders who advise their customers about making investments are not partners in companies whose securities they recommend. Answer: SP=0 (bar over "P" & line thru the equal sign)
3. No pipelines laid across foreign territories are safe investments. Answer: PS=0

16. May 10, 2005

### honestrosewater

Yes.
I don't know- what does the equation and a bar over a letter mean? Are the equations meant to represent the information in the diagrams?

17. May 10, 2005

### kennethj67

I will have to check my textbook which I left at work. So I will let you know tomorrow. Thanks for checking.

18. May 10, 2005

### eternallove29

19. May 11, 2005

### honestrosewater

Now that I look at it, I think I know what they mean. For a class S, (let's underline instead of overline) S denotes the complement of S (all objects x such that x is not in S). For classes S and P, SP denotes the intersection of S and P (all objects x such that x is in S and x is in P). In a Venn Diagram, the complement of circle S is everything outside of S; The intersection of circles S and P is everything inside of the overlap between the circles S and P. The intersection of circle S and P is again eveything inside of the overlap between S and P (everything inside of S and outside of P).
For A propositions, All S are P, there are no objects x such that x is in S and x is not in P, so
SP = 0
For E propositions, No S are P, there are no objects x such that x is in S and x is in P, so
SP = 0
For I propositions, Some S are P, there is at least one object x such that x is in S and x is in P, so
SP > 0
You could say SP $\not=$ 0, but the question asked for inequalities.
For O propositions, Some S are not P, there is at least one object x such that x is in S and x is not in P, so
SP > 0
Notice the relationship between contradictory propositions (A & O) and (E & I).