Descrete Math logic confusion!

Hello everyone.

I'm stuck on this problem. The directions are: In each of 1-4 represent the common form of each argument using letters to stand for component sentences, and fill in the blanks so that the argument in part (b) has the same logical form as the argument in part (a).

#3.

a. This number is even or this number is odd
this number is not even
therefore, this number is odd.

b. ____ or logic is confusing.
my mind is not shot.

there, ____

The books answers are the folloiwng:
common form:
p v q
~p
therefore, q
my mind is shot. logic is confusing.

I understand the first part, p v q, ~p, and therefore, q.

But what i don't understand is why would you put my mind is shot and logic is confusing? Did they not even answer what I was suppose to put in the first blank?

___ or logic is confusing

I'm guessing the reason you would put my mind is shot, is becuase ur taking the negation of the statement becuase above they had ~p. But the therefore, ___ and ___ or logic is confusing doesn't make senes.

Here might be a better example you could explain becuase its more complex.
If n is divisble by 6, then n is divisible by 3.
If n is dividsbile by 3, then the sum of the digits of n is divisble by 3.
Therefore, if n is divisble by 6, then the sum of the digits of n is divisble by 3.

So anytime i saw disvible by 6, i would place a p, anywhere i see divisble by 3 i would put a q and if i see a sum i will put an r.

So i came up with:
if p then q
if q then r
therefore, if p then r

But part b i'm suck on:
If ______________
then the guard condition for the while loop is false.
If_______________
then program executiion moves to the next insrtuction following hte loop.
Therefore, if x equals 0, then ___________
(assume that x is a particluar variable in a particular computer program.

did they just want me to write if p then the guard condition for the while loop is false. If q then program execution moves to next instruction following the loop. THerefore, if x equals 0, then r?
Thanks!
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Recognitions:
 Quote by mr_coffee Hello everyone. I'm stuck on this problem. The directions are: In each of 1-4 represent the common form of each argument using letters to stand for component sentences, and fill in the blanks so that the argument in part (b) has the same logical form as the argument in part (a). #3. a. This number is even or this number is odd this number is not even therefore, this number is odd. b. ____ or logic is confusing. my mind is not shot. there, ____ The books answers are the folloiwng: common form: p v q ~p therefore, q my mind is shot. logic is confusing. I understand the first part, p v q, ~p, and therefore, q. But what i don't understand is why would you put my mind is shot and logic is confusing? Did they not even answer what I was suppose to put in the first blank? ___ or logic is confusing I'm guessing the reason you would put my mind is shot, is becuase ur taking the negation of the statement becuase above they had ~p. But the therefore, ___ and ___ or logic is confusing doesn't make senes.
Let the two blanks be called x and y, and then try to symbolize the argument. Something like:

x or logic is confusing.
my mind is not shot.
therefore, y

Now symbolize this. What would you put for x and y to make the argument form match the way you symbolized the other one?

This seems like an oddly pessimistic problem.

 Here might be a better example you could explain becuase its more complex. If n is divisble by 6, then n is divisible by 3. If n is dividsbile by 3, then the sum of the digits of n is divisble by 3. Therefore, if n is divisble by 6, then the sum of the digits of n is divisble by 3. So anytime i saw disvible by 6, i would place a p, anywhere i see divisble by 3 i would put a q and if i see a sum i will put an r. So i came up with: if p then q if q then r therefore, if p then r But part b i'm suck on: If ______________ then the guard condition for the while loop is false. If_______________ then program executiion moves to the next insrtuction following hte loop. Therefore, if x equals 0, then ___________ (assume that x is a particluar variable in a particular computer program. did they just want me to write if p then the guard condition for the while loop is false. If q then program execution moves to next instruction following the loop. THerefore, if x equals 0, then r? Thanks!
Yes--but then they want you replace p, q, and r with variables so that the argument makes sense (is valid) and follows the form of the other argument.

Here is an example:

It's going to rain or it's not going to rain.
If it rains, I'll study.
If it doesn't rain, I'll go hiking.
Therefore, I will study or go hiking.

This is symbolized
p v q
p --> r
q --> s
Therefore, r v s

Now here's a similar argument:
____ or the town will install a liquid natural gas plant
If the town repairs its roads, ____
If the town installs a liquid natural gas plant, there will be a risk of explosion
Therefore, there will be detours or a risk of explosion

This is symbolized
___1 v q
p --> ____2
q --> s
Therefore, r v s

This argument makes sense and follows the form of the other one only when you have
___1 = p
___2 = r

So then you fill in p and r where the blank spaces were, to get:
The town will repair its roads or the town will install a liquid natural gas plant
If the town repairs its roads, there will be detours
If the town installs a liquid natural gas plant, there will be a risk of explosion
Therefore, there will be detours or a risk of explosion
 Thanks for the explantion! Sorry it took so long to respond, lots of classes :D. i think i understand... I want it in the same form as: if p then q if q then r therefore, if p then r. So... If ________1 then the guard condition for the while loop is false. if _________2 then program execution moves to the next instruction following the loop. Therefore, if x equals 0, then ______3 So if i want to symoblize this now i would get: let "the guard condition for the while looop is false" to be q let "program execution moves to the next instruction following the loop" to be r. let "x equal 0" p. SO i would end up with: If x equals 0 then the guard condition for the while loop is false. If the guard condition for the while looop is false then program execution moves to the next instruction following the loop. Therefore, if x euqals 0, then program execution moves to the next instruction following the loop. I think i got it!