Any Celticsblog math geeks around?

[KungPoweChicken]

If so, it's your lucky day! I've got a question I can't seem to figure out the method to. I'll try and explain the best I can. For a little back round, it is about turning argument statements into symbolic form.

In this case, it is a three statement argument. As usual, the statement will be represented by p,q, and r.

So, let's get to it.

Here is the statement: If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy.


Okay, I get there are three statements; that's not my problem. My problem is that I don't know why p,q,and r are assigned to which statements.

The book provides this as the answer:


                                             (q ^ r) --> p
                                              -p
                                               _________
                                               r --> p

In this case, q is assigned to the statement "Debbie takes vitamins." R is assigned to the statement "Debbie exercises." And p is assigned to the statement "she will be healthy."

I can't figure out why these letters are assigned to these statements. There are several of these statement problems in my book, that follow this formula, and I can't figure out the method to the madness.


So that's my question.

[BballTim]

  First of all, is this really math?

  Secondly:

Here is the statement: If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy.

The book provides this as the answer:


                                             (q ^ r) --> p
                                              -p
                                               _________
                                               r --> p


  Without really understanding what this is or all of the syntax, it looks like a possible typo. I'd expect it to look more like this:

                                             (q ^ r) --> p
                                              -q
                                               _________
                                               r --> p

  That seems to match the statement. If q = "Debbie takes vitamins" and r = "Debbie exercises" and p = "she will be healthy", then if ^ = "and" and --> = "then", "If Debbie takes vitamins and exercises, then she will be healthy" translates to "(q ^ r) --> p". Also "if Debbie exercises, then she will be healthy" translate directly into the 3rd line "r --> p". However, your 2nd line (Debbie is not taking vitamins) should map to -q.

[Fafnir]

Well two degrees in math and playing fantasy insurance pricing makes me a CB math geek. BBalltim has it right, there is a misprint in the answer key or the question.

This is logic, which is used in math and could easily be in a math class.

Functionally those statements don't make any sense however. It does not follow that if (q and r) imply p, not r, thus q implies p.

Unless the problem specifies that Debbie is healthy which from your statement is not the case.

[indeedproceed]

  First of all, is this really math?

  Secondly:

Here is the statement: If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy.

The book provides this as the answer:


                                             (q ^ r) --> p
                                              -p
                                               _________
                                               r --> p


  Without really understanding what this is or all of the syntax, it looks like a possible typo. I'd expect it to look more like this:

                                             (q ^ r) --> p
                                              -q
                                               _________
                                               r --> p

  That seems to match the statement. If q = "Debbie takes vitamins" and r = "Debbie exercises" and p = "she will be healthy", then if ^ = "and" and --> = "then", "If Debbie takes vitamins and exercises, then she will be healthy" translates to "(q ^ r) --> p". Also "if Debbie exercises, then she will be healthy" translate directly into the 3rd line "r --> p". However, your 2nd line (Debbie is not taking vitamins) should map to -q.

To my own understanding...that's the right answer.

It should be -q, right?

[Fafnir]

  First of all, is this really math?

  Secondly:

Here is the statement: If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy.

The book provides this as the answer:


                                             (q ^ r) --> p
                                              -p
                                               _________
                                               r --> p


  Without really understanding what this is or all of the syntax, it looks like a possible typo. I'd expect it to look more like this:

                                             (q ^ r) --> p
                                              -q
                                               _________
                                               r --> p

  That seems to match the statement. If q = "Debbie takes vitamins" and r = "Debbie exercises" and p = "she will be healthy", then if ^ = "and" and --> = "then", "If Debbie takes vitamins and exercises, then she will be healthy" translates to "(q ^ r) --> p". Also "if Debbie exercises, then she will be healthy" translate directly into the 3rd line "r --> p". However, your 2nd line (Debbie is not taking vitamins) should map to -q.

To my own understanding...that's the right answer.

It should be -q, right?

Even then it doesn't make sense unless the problem assumes that Debbie is healthy.

[GreenFaith1819]

I Love this Blog.

There is a wealth of knowledge here. I took Logic and Design 3 terms ago, and while I passed the course I'm not an expert in it by any stretch.

Glad to see there are some experts here in this field.

[Fan from VT]

Questions (I took a logic course in college...8 years ago):

1. remind me what ^ means

2. Are you sure you phrased the wording of the question exactly as written?

3. What is the question they are asking? are they saying that the statement in the question is valid? or are they asking you to determine if the statement is valid? Because as i'm thinking through this, i don't think that the premises and conclusion are valid together.

Here is the statement: If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy.

By my recollection, such a statement should look something like:

P=Vitamins
q=exercise
r=healthy

(As far as I remember, the actual lettering and assignment of p,q,r is arbitrary and should be defined for each new problem, yeah?)

1. (p & q) --->  r
2. -p
___________________
[therefore] q ---> r

So then you would need a truth table for 3 conditions:

P Q R
T T T
T T F
T F T
F T T
T F F
F T F
F F T
F F F

Then you go through line by line.
-Premise one allows you to eliminate line #2 (TTF is not valid if (p & q) ---> r is True.)
-Premise 2 allows you to eliminate lines 1, 2, 3, 5 (Premise 2, by definition, says that p is false).

So we are left with 4,6,7,8. The Conclusion is q ---> r. so we can eliminate 7 and 8 because they do not apply to the truth of the statement q ---> r.

Therefore, the statement I wrote from your question is saying that the premises from the question are implying that lines 4 and 6 are True. However, clearly line 6 (when q is true and r is not true) violates the conclusion q ---> r, so it appears to me as though this argument is NOT valid.

This is fun... and quite a memory stretch, so please write back after triple checking the wording of the question and also clarifying exactly what your book is asking/saying: are they telling you it IS a valid statement? are they asking you to determine if it is a valid statement? and what does ^ mean?

[KungPoweChicken]

  First of all, is this really math?

  Secondly:

Here is the statement: If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy.

The book provides this as the answer:


                                             (q ^ r) --> p
                                              -p
                                               _________
                                               r --> p


  Without really understanding what this is or all of the syntax, it looks like a possible typo. I'd expect it to look more like this:

                                             (q ^ r) --> p
                                              -q
                                               _________
                                               r --> p

  That seems to match the statement. If q = "Debbie takes vitamins" and r = "Debbie exercises" and p = "she will be healthy", then if ^ = "and" and --> = "then", "If Debbie takes vitamins and exercises, then she will be healthy" translates to "(q ^ r) --> p". Also "if Debbie exercises, then she will be healthy" translate directly into the 3rd line "r --> p". However, your 2nd line (Debbie is not taking vitamins) should map to -q.

Yes you are right. The answer is supposed to be -q. That was a typo on my part, not the book.


The problem I am having is that I'm not getting why the letters are assigned to the statements. In the original post I gave that information, but in the problems that information is not given, only the argument.

For example, using the same argument: "If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy."  

I don't understand why r couldn't represent the statement "she is healthy." Why can't q represent "Debbie exercises." And why can't r represent "Debbie takes vitamins." Finding the correct answer completely relies on finding out how to assign the correct letter to the correct statement. Symbolically expressing the answer is fairly easy after that. But I can't seem to figure it out. Assigning the letters to the statement seems completely arbitrary to me.



I have another problem, if you or any one else, wants to take a crack at it. It's another three statement argument. Again, if anyone knows how to do this, it would be nice to know how you arrive at why you are assigning what letter to what statement.


Here's another problem:


"If I study for two hours, I get tired or irritable. I am studying for two hours and not getting irritable. Therefore, I am not getting tired.



Is this stuff math? It's supposed to be "logic" math.

[Fan from VT]

  First of all, is this really math?

  Secondly:

Here is the statement: If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy.

The book provides this as the answer:


                                             (q ^ r) --> p
                                              -p
                                               _________
                                               r --> p


  Without really understanding what this is or all of the syntax, it looks like a possible typo. I'd expect it to look more like this:

                                             (q ^ r) --> p
                                              -q
                                               _________
                                               r --> p

  That seems to match the statement. If q = "Debbie takes vitamins" and r = "Debbie exercises" and p = "she will be healthy", then if ^ = "and" and --> = "then", "If Debbie takes vitamins and exercises, then she will be healthy" translates to "(q ^ r) --> p". Also "if Debbie exercises, then she will be healthy" translate directly into the 3rd line "r --> p". However, your 2nd line (Debbie is not taking vitamins) should map to -q.

Yes you are right. The answer is supposed to be -q. That was a typo on my part, not the book.


The problem I am having is that I'm not getting why the letters are assigned to the statements. In the original post I gave that information, but in the problems that information is not given, only the argument.

For example, using the same argument: "If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy."  

I don't understand why r couldn't represent the statement "she is healthy." Why can't q represent "Debbie exercises." And why can't r represent "Debbie takes vitamins." Finding the correct answer completely relies on finding out how to assign the correct letter to the correct statement. Symbolically expressing the answer is fairly easy after that. But I can't seem to figure it out. Assigning the letters to the statement seems completely arbitrary to me.



I have another problem, if you or any one else, wants to take a crack at it. It's another three statement argument. Again, if anyone knows how to do this, it would be nice how you arrive at why you are assigning what letter to what statement.


Here's another problem:


"If I study for two hours, I get tired or irritable. I am studying for two hours and not getting irritable. Therefore, I am not getting tired.



Is this stuff math? It's supposed to be "logic" math.

FALSE!

[Fan from VT]

  First of all, is this really math?

  Secondly:

Here is the statement: If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy.

The book provides this as the answer:


                                             (q ^ r) --> p
                                              -p
                                               _________
                                               r --> p


  Without really understanding what this is or all of the syntax, it looks like a possible typo. I'd expect it to look more like this:

                                             (q ^ r) --> p
                                              -q
                                               _________
                                               r --> p

  That seems to match the statement. If q = "Debbie takes vitamins" and r = "Debbie exercises" and p = "she will be healthy", then if ^ = "and" and --> = "then", "If Debbie takes vitamins and exercises, then she will be healthy" translates to "(q ^ r) --> p". Also "if Debbie exercises, then she will be healthy" translate directly into the 3rd line "r --> p". However, your 2nd line (Debbie is not taking vitamins) should map to -q.

Yes you are right. The answer is supposed to be -q. That was a typo on my part, not the book.


The problem I am having is that I'm not getting why the letters are assigned to the statements. In the original post I gave that information, but in the problems that information is not given, only the argument.

For example, using the same argument: "If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy."  

I don't understand why r couldn't represent the statement "she is healthy." Why can't q represent "Debbie exercises." And why can't r represent "Debbie takes vitamins." Finding the correct answer completely relies on finding out how to assign the correct letter to the correct statement. Symbolically expressing the answer is fairly easy after that. But I can't seem to figure it out. Assigning the letters to the statement seems completely arbitrary to me.



I have another problem, if you or any one else, wants to take a crack at it. It's another three statement argument. Again, if anyone knows how to do this, it would be nice to know how you arrive at why you are assigning what letter to what statement.


Here's another problem:


"If I study for two hours, I get tired or irritable. I am studying for two hours and not getting irritable. Therefore, I am not getting tired.



Is this stuff math? It's supposed to be "logic" math.

I would ask your teacher this question explicitly. My instinct was to use p,q,r in alphabetical order to represent statements in the order in which they appeared in the question. Are you sure that there is only one "right" answer? or is any answer acceptable as long as it's consistent? Since the variables p,q,r are empty until assigned, i think the assigning is implied by the first line, then you have to be consistent. so if the first line is

p^q -> r

you have to have

-p
______
q -> r


I would think that that is just as correct as

r^q  --> p
-r
________
q---> p.



But ask your teacher.

[BballTim]

  First of all, is this really math?

  Secondly:

Here is the statement: If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy.

The book provides this as the answer:


                                             (q ^ r) --> p
                                              -p
                                               _________
                                               r --> p


  Without really understanding what this is or all of the syntax, it looks like a possible typo. I'd expect it to look more like this:

                                             (q ^ r) --> p
                                              -q
                                               _________
                                               r --> p

  That seems to match the statement. If q = "Debbie takes vitamins" and r = "Debbie exercises" and p = "she will be healthy", then if ^ = "and" and --> = "then", "If Debbie takes vitamins and exercises, then she will be healthy" translates to "(q ^ r) --> p". Also "if Debbie exercises, then she will be healthy" translate directly into the 3rd line "r --> p". However, your 2nd line (Debbie is not taking vitamins) should map to -q.

Yes you are right. The answer is supposed to be -q. That was a typo on my part, not the book.


The problem I am having is that I'm not getting why the letters are assigned to the statements. In the original post I gave that information, but in the problems that information is not given, only the argument.

For example, using the same argument: "If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy."  

I don't understand why r couldn't represent the statement "she is healthy." Why can't q represent "Debbie exercises." And why can't r represent "Debbie takes vitamins." Finding the correct answer completely relies on finding out how to assign the correct letter to the correct statement. Symbolically expressing the answer is fairly easy after that. But I can't seem to figure it out. Assigning the letters to the statement seems completely arbitrary to me.

  Again, I'm no expert, but it is arbitrary, right? I just deduced which letter went with which statement based on matching the statements to the equation.

                                             (q ^ r) --> p
                                              -q
                                               _________
                                               r --> p
and

                                             (p ^ q) --> r
                                              -p
                                               _________
                                               q --> r

  are identical, they just assign a different letter to the three statements.

[Fan from VT]

man it's slow typing these responses in syntax; no wonder there have already been repeat posts! expect more...

[LooseCannon]

Assigning the letters to the statement seems completely arbitrary to me.

Consider it arbitrary.

What book are you getting these problems from?  It seems like you are on an early chapter where you are just concentrating on translating statements into logical notation but not yet to the part of the book where you learn about evaluating statements.  Once you get to that part, it might be more obvious how logic is math.

[KungPoweChicken]

  First of all, is this really math?

  Secondly:

Here is the statement: If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy.

The book provides this as the answer:


                                             (q ^ r) --> p
                                              -p
                                               _________
                                               r --> p


  Without really understanding what this is or all of the syntax, it looks like a possible typo. I'd expect it to look more like this:

                                             (q ^ r) --> p
                                              -q
                                               _________
                                               r --> p

  That seems to match the statement. If q = "Debbie takes vitamins" and r = "Debbie exercises" and p = "she will be healthy", then if ^ = "and" and --> = "then", "If Debbie takes vitamins and exercises, then she will be healthy" translates to "(q ^ r) --> p". Also "if Debbie exercises, then she will be healthy" translate directly into the 3rd line "r --> p". However, your 2nd line (Debbie is not taking vitamins) should map to -q.

Yes you are right. The answer is supposed to be -q. That was a typo on my part, not the book.


The problem I am having is that I'm not getting why the letters are assigned to the statements. In the original post I gave that information, but in the problems that information is not given, only the argument.

For example, using the same argument: "If Debbie takes vitamins and exercises, then she will be healthy. Debbie is not taking vitamins. Therefore, if Debbie exercises, then she will be healthy."  

I don't understand why r couldn't represent the statement "she is healthy." Why can't q represent "Debbie exercises." And why can't r represent "Debbie takes vitamins." Finding the correct answer completely relies on finding out how to assign the correct letter to the correct statement. Symbolically expressing the answer is fairly easy after that. But I can't seem to figure it out. Assigning the letters to the statement seems completely arbitrary to me.

  Again, I'm no expert, but it is arbitrary, right? I just deduced which letter went with which statement based on matching the statements to the equation.

                                             (q ^ r) --> p
                                              -q
                                               _________
                                               r --> p
and

                                             (p ^ q) --> r
                                              -p
                                               _________
                                               q --> r

  are identical, they just assign a different letter to the three statements.

Ah yes, I think I'm getting it down now. The letters are arbitrary, but you've got to look for consistency--good call. This is actually really evident in my book because these particular questions give a multiple choice format--so you just more or less, look for consistency.

But if these weren't multiple choice, the letters wouldn't matter, and I think that's what I was getting hung up on--trying to figure out how I would get the "right letters." When it turns out, there are no right letters! I'm surprised I didn't get this before.

Thank you all Celticsbloggers for your help.

[BballTim]

I think that's what I was getting hung up on--trying to figure out how I would get the "right letters." When it turns out, there are no right letters! 

  Strictly speaking, there are no "wrong letters", all the letters are right. But I digress.