Q22

[hyewonkim89]

This question threw me off.

I just changed up my diagram (O <-> N) and tried to come up with two frames: O in S and N in R & N in S and O in R.

When I put N in S and O in R, I could figure out where every element went. So I could eliminate B through E. But I still can't figure out why A must be true.

Please help!

[patrice.antoine]

From the fourth rule we know that if N is in (r) then O is also in (r):

N(r) --> O(r)

The contrapositive of this is if O is in (s) then N is in (s):

O(s) --> N(s)


The question presents us with both N and O being in different clinics which would mean we cannot place N in (r) or O in (s) as that would result in violating what we are being asked. As such, we know that N must be in (s) and O in (r) as part of our set up.

Does N being in (s) and O in (r) trigger any other chains??

It does!

We know that if N is in (s), L is in (r).

and

if O is in (r), J is in (s), K is in (r) and P is in (s). Therefore, answer choice (A) must be true.

The last trigger was formed by combining the contrapositives of the the first two rules and the last rule. Here are how I wrote my rules out in the order presented:

Conditional Rules:

1. J(s)---> K(r)
2. J(r) ---> O(s)
3. L(s) ---> N(r) and P(r)
4. N(r) ---> O(r)
5. P(r)---> K(s) and O(s)

Contrapositives:

1. K(s)---> J(r)
2. O(r) ---> J(s)
3. N(s) OR P(s) ---> L(r)
4. O(s) ---> N(s)
5. K(r) OR O(r)---> P(s)


Transitive (Combined) Conditionals

1. J(s)---> K(r)---> P(s)
2. J(r) ---> O(s)---> N(s)
3. O(r) ---> J(s)---> K(r)---> P(s)
4. P(r)---> K(s) and O(s)---> N(s)
5. L(s) ---> N(r) and P(r) ---> O(r), K(s) and O(s)

For the last transitive property conditionals, we can note a violation. If we have both N and P in (r), that will result in O having to be in both (r) and (s). As such, we know for certain N and P cannot both be in (r). This helps us answer question (23) along the process.


I hope this helps!!!

[hyewonkim89]

Wow this really helps a lot!

Instead of putting N in S and O in R, I just changed up my original diagram and just confused the crap out of myself

Thank you so much!