About a case of logic

[safwane]

I have three sets A,B,C in which the following case is impossible (wrong):

A is finite and B is finite and C is infinite.

I want to see the true case. My idea is: The true case is: A is infinite or B is infinite or C is finite. However, I have some doubts on that

 

[JeffM]

It is not true (false) that A is finite and B is finite and C is infinite.

Therefore it is true that A is not finite or B is not finite or C is not infinite

Therefore, it is true that A is infinite or B is infinite or C is finite.

In the notation of propositional calculus
[math]\neg (p \land q) \iff \neg p \lor \neg q.[/math]
where [imath]\neg[/imath] means ”it is false that,” [imath]\land[/imath] means “and,” and [imath]\lor[/imath] means “INCLUSIVE or.”

It is one of DeMorgan‘s Laws. The other is

[math]\neg(p \lor q) \iff \neg p \land \neg q.[/math]

 

[lev888]

I have three sets A,B,C in which the following case is impossible (wrong):

A is finite and B is finite and C is infinite.

I want to see the true case. My idea is: The true case is: A is infinite or B is infinite or C is finite. However, I have some doubts on that

There is nothing impossible about this case:
e.g. A is 1, 2. B is 3, 4. C is the set of natural numbers.
To make it impossible you need to provide more info about the sets and relationships among them.

 

[JeffM]

There is nothing impossible about this case:
e.g. A is 1, 2. B is 3, 4. C is the set of natural numbers.
To make it impossible you need to provide more info about the sets and relationships among them.

@lev888

I read the question that way at first too.

I think, however, that it is badly worded question along the line of whether two propositions are equivalent.

 

[pka]

I have three sets A,B,C in which the following case is impossible (wrong):
A is finite and B is finite and C is infinite.
I want to see the true case. My idea is: The true case is: A is infinite or B is infinite or C is finite. However, I have some doubts on that

The question is so poorly worded as to make it utter rubbish.
There is no relationship stated among the three sets.
Their induvial cardinalates have nothing to do with the question as posted.
Did you mean to include something about subset inclusion?

 

[Deleted member 4993]

I have three sets A,B,C in which the following case is impossible (wrong):

A is finite and B is finite and C is infinite.

I want to see the true case. My idea is: The true case is: A is infinite or B is infinite or C is finite. However, I have some doubts on that

Suppose A is the set of edible items in my refrigerator

B is the set of books in my book-shelf

C is the set of tool in a plumber's tool-box.

There - C cannot be infinite.

 

[Dr.Peterson]

I have three sets A,B,C in which the following case is impossible (wrong):

A is finite and B is finite and C is infinite.

I want to see the true case. My idea is: The true case is: A is infinite or B is infinite or C is finite. However, I have some doubts on that

To try to reword this so that it makes sense (and assuming, as I believe, that JeffM is reading it rightly), I would say this:

Given three sets A, B, and C, if it is known to be false that "A is finite and B is finite and C is infinite", then what can we say is necessarily true?​

Does that sound like what you understand it to mean?

 

[safwane]

There is nothing impossible about this case:
e.g. A is 1, 2. B is 3, 4. C is the set of natural numbers.
To make it impossible you need to provide more info about the sets and relationships among them.

The question is so poorly worded as to make it utter rubbish.
There is no relationship stated among the three sets.
Their induvial cardinalates have nothing to do with the question as posted.
Did you mean to include something about subset inclusion?

This is just an exercice of logic

 

[pka]

This is just an exercise of logic

As someone who taught logic courses for forty+ years, I tell you that is not an exercise of logic.
In fact the numerical size of sets is hardily ever taught in beginning logic.
Please post the name of your text as well its author.

 

[safwane]

As someone who taught logic courses for forty+ years, I tell you that is not an exercise of logic.
In fact the numerical size of sets is hardily ever taught in beginning logic.
Please post the name of your text as well its author.

It is an exercice in arabic from Batna university, Algeria

 

[safwane]

To try to reword this so that it makes sense (and assuming, as I believe, that JeffM is reading it rightly), I would say this:

Given three sets A, B, and C, if it is known to be false that "A is finite and B is finite and C is infinite", then what can we say is necessarily true?​

Does that sound like what you understand it to mean?

Yes. It is.

 

[Dr.Peterson]

Yes. It is.

Good. That means that this is in fact just about logic, as your title said, and not about set theory or about infinity.

It is an exercice in arabic from Batna university, Algeria

It would not be a bad idea to include the original exercise, in the original language, if that can be done in a form that we could try translating without having to know the language (or if there are any regular contributors here who know Arabic!). That can help us clarify the meaning.

In any case, I hope you are convinced now that your answer was correct, and why!

 

[Steven G]

There is nothing impossible about this case:
e.g. A is 1, 2. B is 3, 4. C is the set of natural numbers.
To make it impossible you need to provide more info about the sets and relationships among them.

Lev,
You know better than this! Since A is a set we do not write A=1, rather we write A = {1}. Same with B. Since you said that C is a set of natural number, that is fine.
Steven

 

[lev888]

Lev,
You know better than this! Since A is a set we do not write A=1, rather we write A = {1}. Same with B. Since you said that C is a set of natural number, that is fine.
Steven

I didn't write A=1.