Nec & Suff Drills

[theli]

I tried to graph the following drills but my method never seems to lead to the correct answer in the Tm book.

Example One :

P:All M's are N's
P:Some M's are not O's
C: ??

a) Most N'a are O's
b) All N's are M's
c) Not all O's are N's
d) Most O's are M's
e) Not all N's are O's

-----------------------

Example Two:

P: All G's are L's
P: All H's are K's
P: No L's are K's
C: ??

a) Some G's are K's
b) All H's are G's
c) Not all K's are H's
d) No G's are H's
e) All K's are both G's H's

Thank you!
Theli

[desmo]

you know some n's are not o's

isn't this saying e) not all n's are o's

you know g = l, h = k, l dne k therefore g dne h (d)

[AaronJ]

When going from an all to a some statement, as long as the some statement contains one of the variables that occur in the necessary side of the all stament then you can derive another some statment from the combination of the sufficient all condition and the other variable in the some statement. Fewwww.  Look at it this way

if all M's are N's you could have:

MMM
NNNNNN

If some M's are not O's then:
 
  000000000
MMM
NNNNNN

Which shows that some N's are not O's

For the second example it works like this

G-->L
H-->k
L-->not K

the only valid conclusion as given is then

G-->not H

because

G to L to not K

contrapositive of the third P is not K to not H

so G-->not H

[magicmatttt]

When going from an all to a some statement, as long as the some statement contains one of the variables that occur in the necessary side of the all stament then you can derive another some statment from the combination of the sufficient all condition and the other variable in the some statement. Fewwww.  Look at it this way

if all M's are N's you could have:

MMM
NNNNNN

If some M's are not O's then:
 
  000000000
MMM
NNNNNN

Which shows that some N's are not O's

For the second example it works like this

G-->L
H-->k
L-->not K

the only valid conclusion as given is then

G-->not H

because

G to L to not K

contrapositive of the third P is not K to not H

so G-->not H

 I hate those question types.  Fortunately I don't think they appear too often, or do they?

[AaronJ]

Yes actually they do seem to come up fairly often.  You should definetly practice working with conditional statements and get good at it.  You are likely to see several questions that contain either an argument or a set of facts and then are asked to identify "what must be true".  Often times your intuition will be enough, if you are that sort of person, but in other cases things will just be to complicated to rely on intuition and thus you will need to know how to manipulate the conditions the get the true result.