Any Celticsblog math geeks around?

[action781]

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.

Hi KungPowe,

B.A. and M.A.T. in Mathematics here, currently a math teacher.  Last took logic back in 2003ish though, but still think I can help.

As a teacher, I'm very glad to see that you seem to be getting the assignment of variables.  Let me post a complete solution to your 2nd question that you can check your work with after.  I don't have an upside down karat for "or" so i'll just write it as "or".

So the statements are:
"I study for two hours", "I get tired", "I get irritable"

Lets name them:
"I study for two hours" = p
"I get tired" = q
"I get irritable" = r

The first sentence states: "If I study for two hours, I get tired or irritable."

So in logic, that would be written as "if p, then q or r" and in symbol notation:  p --> (q "or" r) commonly stated as "p implies q or r"

The second: "I am studying for two hours and not getting irritable."

So in logic, that would be said "p and not r" which in symbol notation:  p ^ -r

The third:  "Therefore, I am not getting tired."

In logic, "not q" or -q

So the system (I've never written it like this) appears like it should be:

 p --> (q "or" r)
p ^ -r
________________
-q

And yeah, this logic is math and incredibly important in the use of proofs in advanced Algebra and Analysis.  And it will help you answer the very important question of whether or not every pink elephant in your classroom can fly or not.   

Check to see if that problem was written correctly though...

[Fan from VT]

Sorry, It looks like I was jumping the gun with my posts and actually trying to figure out if the statements were valid, and not just focusing on translating the statements into syntax form.


Have you done work on validity yet? Truth tables?

[Fan from VT]

Sorry, It looks like I was jumping the gun with my posts and actually trying to figure out if the statements were valid, and not just focusing on translating the statements into syntax form.


Have you done work on validity yet? Truth tables?

action781 did a nice job of translating the studying problem into syntax; when I had given my answer of "False" I was talking about whether the validity of the entire statement stood up. I'll write out that logic below so others can correct me if wrong. It's been a long time since logic class.


So my understanding is that you have to create a truth table for however many variables you have. Then the goal of a logic statement like the one you provide is to see if the conclusion is necessarily implied by the premises; in other words if the premises are true, then as you eliminate lines from your truth table, if you are left only with truth table statements that fit with the conclusion, your statement is valid.

Here's the truth table: either variable may be true or false.

Line: Study(p)/Tired(q)/Irritable(r)   1         T            T         T   2         T            T         F   3         T            F         T   4         F            T         T   5         T            F         F   6         F            T         F   7         F            F         T   8         F            F         F

Now we write it out in syntax:
p=Studying 2 hrs
q=tired
r=irritated

Premise 1: p --> (q V r)
Premise 2: p ^ -r
___________________
Conclusion: -q

If premise 1 is true, we can really only eliminate line #5 from our truth table: line 5 says yes we've studied, but we are neither tired nor annoyed, which violates premise 1.

If premise 2 is true, we can only keep lines that have a T under "study" and an F under "irritable." So eliminate 1, 3, 4, 6, 7, 8

Therefore, from premises 1 + 2, we have eliminated all but line #2. The conclusion is "Not q", but our only remaining truth line has q to be True; therefore the conclusion is NOT implied by the premises, and the statement is false.

Thoughts?

[Fafnir]

You've got it right Fan from VT.