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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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# Descrete Math logic confusion!

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