Double Not Arrow Vs Double Arrow with a slash on one

[Dave Killoran]

This addresses the following question:

I'm on chapter 13 of the LR bible power score and I can't seem to understand what's the difference between double not arrow and a double arrow with a dash in the middle of the letter

If I'm following this correctly, you mean the difference between two statements like the following:

• C O
  
  and
  
  C O

With any pair of variables, there are four possible outcomes, which I'll use to explain what's happening

1. C and O — both occur
2. C and O — one occurs and the other does not
3. C and O — one occurs and the other does not
4. C and O — both do not occur


Now let's look at each statement and see what happens:

• C O
  
  In this relationship, exactly one outcome is impossible: that both C and O occur (that's the first option above).
  
  That means that each of the following is possible:
  
  2. C and O
  3. C and O
  4. C and O

Now let's look at the other relationship:

• C O
  
  In this relationship, C and O are always together, so you must have either C and O, or that pair can't occur, meaning you'd have C and O.
  
  That means that each of the following is possible:
  
  2. C and O
  3. C and O
  
  
  In other words, both happening or both not happening is impossible, which means that the first and fourth options above can't happen).

Hopefully I understood your reference to the diagrams and explained the right relationships correctly. If not, just let me know!

[sohaatiq]

Hi Dave,

I understand your explanation! Would you be able to provide a question stem that would lead to a C /O inference?

[Jeremy Press]

Hi sohaatiq,

LSAC would likely word a rule leading to the C O diagram in the following way:

"When C is selected, O is not selected. Otherwise, O is selected."

The first part of the rule ("When C is selected, O is not selected") gives us the straightforward diagram running from C to O, the part that maps as: C O.

The second part of the rule begins with an "otherwise," which when LSAC includes it in this construction indicates that the sufficient condition (C is selected) did NOT occur. In other words, the second part of the rule is saying that when C is not selected, O is selected. That would diagram this way: C O. But that rule also implies its contrapositive: O C, which is where we get the validation for running the arrow in the opposite direction (from O backward to C).

Let me know if that clarifies!