# Syllogistic Logic: method to find out the truth value of propositions

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I am preparing for my logic exam and I would like to ask what would be the proper strategy to find the truth or falsehood of the propositions.

Example of a question:

If “No scientists are philosophers” is true, what may be inferred about the truth or falsehood of the following propositions? That is, which can be known to be true, which can be known to be false, and which are undetermined?

*1. No nonphilosophers are scientists.

*5. No nonscientists are nonphilosophers.

*10. No philosophers are nonscientists.

My answer is 1,5,10 all undetermined. (I draw out Venn diagram and compare them)

However, the textbook said that 1 = F, 5= undetermined, 10= false

how should I approach the question??

updated with my working:

I consider there are two ways to deal with the questions

1. with existential Import

- with existential import meaning there exist at least one thing in the circle, so now I know the overlapping area between S and P is empty, so

q1 false

q5 undetermined

q10 false

2. without the asuumption of existential import

- since i only know that overlapping area of the S and P is empty , the other graphs's truth value cannot be determined by logic

so i choose all q to be undetermined

above is my working process, but I am not really sure about if i approach the question ( using Existential import ) in a CORRECt way though.

Thanks for helping !!

Example of a question:

If “No scientists are philosophers” is true, what may be inferred about the truth or falsehood of the following propositions? That is, which can be known to be true, which can be known to be false, and which are undetermined?

*1. No nonphilosophers are scientists.

*5. No nonscientists are nonphilosophers.

*10. No philosophers are nonscientists.

My answer is 1,5,10 all undetermined. (I draw out Venn diagram and compare them)

However, the textbook said that 1 = F, 5= undetermined, 10= false

how should I approach the question??

updated with my working:

I consider there are two ways to deal with the questions

1. with existential Import

- with existential import meaning there exist at least one thing in the circle, so now I know the overlapping area between S and P is empty, so

q1 false

q5 undetermined

q10 false

2. without the asuumption of existential import

- since i only know that overlapping area of the S and P is empty , the other graphs's truth value cannot be determined by logic

so i choose all q to be undetermined

above is my working process, but I am not really sure about if i approach the question ( using Existential import ) in a CORRECt way though.

***and i am confused whether I can still apply the same approach if the given proposition is FALSE (instead of true) ??**Thanks for helping !!

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#2

(Original post by

I am preparing for my logic exam and I would like to ask what would be the proper strategy to find the truth or falsehood of the propositions.

Example of a question:

If “No scientists are philosophers” is true, what may be inferred about the truth or falsehood of the following propositions? That is, which can be known to be true, which can be known to be false, and which are undetermined?

*1. No nonphilosophers are scientists.

*5. No nonscientists are nonphilosophers.

*10. No philosophers are nonscientists.

My answer is 1,5,10 all undetermined. (I draw out Venn diagram and compare them)

However, the textbook said that 1 = F, 5= undetermined, 10= false

how should I approach the question??

**yoongijust**)I am preparing for my logic exam and I would like to ask what would be the proper strategy to find the truth or falsehood of the propositions.

Example of a question:

If “No scientists are philosophers” is true, what may be inferred about the truth or falsehood of the following propositions? That is, which can be known to be true, which can be known to be false, and which are undetermined?

*1. No nonphilosophers are scientists.

*5. No nonscientists are nonphilosophers.

*10. No philosophers are nonscientists.

My answer is 1,5,10 all undetermined. (I draw out Venn diagram and compare them)

However, the textbook said that 1 = F, 5= undetermined, 10= false

how should I approach the question??

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(Original post by

Firstly, what did you get for your Venn diagram?

**ghostwalker**)Firstly, what did you get for your Venn diagram?

I consider there are two ways to deal with the questions

1. with existential Import

- with existential import meaning there exist at least one thing in the circle, so now I know the overlapping area between S and P is empty, so

q1 false

q5 undetermined

q10 false

2. without the asuumption of existential import

- since i only know that overlapping area of the S and P is empty , the other graphs's truth value cannot be determined by logic

so i choose all q to be undetermined

above is my working process, but I am not really sure about if i approach the question ( using Existential import ) in a CORRECt way though.

and i am confusd whether I can still apply the same approach if the given proposition isFALSE (instead of true) ??

Thanks for helping !!

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#4

q5 is undetermined because we do not know whether the sets "Scientists" and "Philosophers" are exhaustive.

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#5

(Original post by

...

**yoongijust**)...

It's clear from the given answers that they are assuming both the sets, philosophers and scientists, are not empty.

I notice from the numbering of the questions that these are just three of the ten. Are the other questions thrown into confusion if you don't assume "Existential import"? And what is the significance of the the "*"? I can see a snapshot of the book online, but only small bits of it - not enough to explain the "*"

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#6

(Original post by

I consider there are two ways to deal with the questions

1. with existential Import

- with existential import meaning7 there exist at least one thing in the circle, so now I know the overlapping area between S and P is empty, so

q1 false

q5 undetermined

q10 false

2. without the asuumption of existential import

- since i only know that overlapping area of the S and P is empty , the other graphs's truth value cannot be determined by logic

so i choose all q to be undetermined

above is my working process, but I am not really sure about if i approach the question ( using Existential import ) in a CORRECt way though.

and i am confusd whether I can still apply the same approach if the given proposition isFALSE (instead of true) ??

Thanks for helping !!

**yoongijust**)I consider there are two ways to deal with the questions

1. with existential Import

- with existential import meaning7 there exist at least one thing in the circle, so now I know the overlapping area between S and P is empty, so

q1 false

q5 undetermined

q10 false

2. without the asuumption of existential import

- since i only know that overlapping area of the S and P is empty , the other graphs's truth value cannot be determined by logic

so i choose all q to be undetermined

above is my working process, but I am not really sure about if i approach the question ( using Existential import ) in a CORRECt way though.

and i am confusd whether I can still apply the same approach if the given proposition isFALSE (instead of true) ??

Thanks for helping !!

There is another way of showing that 1 and 10 are false. Think about the obverse and the simple converse of the proposition you've been given.

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(Original post by

"No scientists are philosophers" is an E proposition (i.e. of the form 'no S is P' so unless you've been explicitly asked to use Aristotelian logic in your assignment, this proposition does not necessarily have existential import because it is a general statement rather than a particular one. If it were "some scientists are philosophers" you could safely say that it has existential import, but that isn't the case in your question, so I would steer clear of approaches involving existential import.

There is another way of showing that 1 and 10 are false. Think about the obverse and the simple converse of the proposition you've been given.

**Sonechka**)"No scientists are philosophers" is an E proposition (i.e. of the form 'no S is P' so unless you've been explicitly asked to use Aristotelian logic in your assignment, this proposition does not necessarily have existential import because it is a general statement rather than a particular one. If it were "some scientists are philosophers" you could safely say that it has existential import, but that isn't the case in your question, so I would steer clear of approaches involving existential import.

There is another way of showing that 1 and 10 are false. Think about the obverse and the simple converse of the proposition you've been given.

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#8

(Original post by

so you mean that even without the assumption of existential import, the answers are 1.False, 5.undetermined, 10.False ?

**yoongijust**)so you mean that even without the assumption of existential import, the answers are 1.False, 5.undetermined, 10.False ?

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(Original post by

Yes. Do you understand why, given the hints I just gave? (Tell me if you don't understand them.)

**Sonechka**)Yes. Do you understand why, given the hints I just gave? (Tell me if you don't understand them.)

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#10

(Original post by

I don't understand sorry

**yoongijust**)I don't understand sorry

The obverse of a proposition is the logically equivalent proposition derived from negating its subject and predicate terms, so "no S are P" becomes "all S are non-P." If a proposition is true then its obverse is also true. You should now be able to see why the proposition in q1 is false, judging by its obverse.

For question 10, the proposition we're dealing with is what's called an E proposition, meaning that it's of the form "No S is P" as I mentioned earlier. For this type of proposition, if "No S is P" is true then "No P is S" (known as the simple converse of the proposition) is also true. So if it is true that "no scientists are philosophers", it is also true that "no philosophers are scientists." How do you know now that statement 10 is false?

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(Original post by

Don't worry, I don't know what you've covered on your course so far so you'll probably learn this at some point in the future I'll explain it anyway so that you can understand the questions but if you don't get it, it might just be something to come back to.

The obverse of a proposition is the logically equivalent proposition derived from negating its subject and predicate terms, so "no S are P" becomes "all S are non-P." If a proposition is true then its obverse is also true. You should now be able to see why the proposition in q1 is false, judging by its obverse.

For question 10, the proposition we're dealing with is what's called an E proposition, meaning that it's of the form "No S is P" as I mentioned earlier. For this type of proposition, if "No S is P" is true then "No P is S" (known as the simple converse of the proposition) is also true. So if it is true that "no scientists are philosophers", it is also true that "no philosophers are scientists." How do you know now that statement 10 is false?

**Sonechka**)Don't worry, I don't know what you've covered on your course so far so you'll probably learn this at some point in the future I'll explain it anyway so that you can understand the questions but if you don't get it, it might just be something to come back to.

The obverse of a proposition is the logically equivalent proposition derived from negating its subject and predicate terms, so "no S are P" becomes "all S are non-P." If a proposition is true then its obverse is also true. You should now be able to see why the proposition in q1 is false, judging by its obverse.

For question 10, the proposition we're dealing with is what's called an E proposition, meaning that it's of the form "No S is P" as I mentioned earlier. For this type of proposition, if "No S is P" is true then "No P is S" (known as the simple converse of the proposition) is also true. So if it is true that "no scientists are philosophers", it is also true that "no philosophers are scientists." How do you know now that statement 10 is false?

ummm How about a question with existential import?

can I still use venn diagram find out the answer in question requiring existential import？

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