Conditional Reasoning Clarification

[obs23]

Example from CR chapter of LR bible (p.155).

"It is either feast or famine. "

Diagram:
Fe = feast Fa = famine

Fe --> ~Fa
Fa --> ~Fe

~Fe --> Fa
~Fa --> Fe

Question: Can the above relationship be summarized into Fe Fa, and in if so, would it mean the same thing as diagrams above or are these equivalent? I am just a little confused by all these arrow diagramming.

Thanks for help.

[Dave Killoran]

Hi Obs,

The Fe Fa diagram reflects the relationship in the first pair of diagrams. that diagram means that the two can never occur together.

There is a different diagram for the second set, and that diagram would be:

Fe Fa

That diagram means that both can never be absent (and thus that at least one must occur).

When both diagrams are combined, we can infer that one and exactly one of the two always occurs.

Please let me know if that helps. Thanks!

[obs23]

Makes sense. it is funny I did not know that other diagram could exist at all, but then when I see it, I am like "why would not it?"

This is incredibly helpful. I know it may not be the case for others but this is really great! It is like I read your bible, but some bits and pieces need to come together when I practice, especially since when you begin practicing all concepts begin to combine and you need to recognize all that you have learned and it is easy to get confused. Anyways, lots of kudos.

Thanks a lot,
obs

[Dave Killoran]

Awesome, it's great hear that this is helping. Thanks!

[momgoingbacktoschool]

Hi Obs,

The Fe Fa diagram reflects the relationship in the first pair of diagrams. that diagram means that the two can never occur together.

There is a different diagram for the second set, and that diagram would be:

Fe Fa

That diagram means that both can never be absent (and thus that at least one must occur).

When both diagrams are combined, we can infer that one and exactly one of the two always occurs.

Please let me know if that helps. Thanks!

Hello,

so is the double negative diagram correct? in the answer section to this question, it isn't shown as the correct response.

[Dave Killoran]

Hi Mom,

Thanks for the question! Remember, the double-not arrows are summations of relationships. So, this diagram:

• Fe Fa

Is actually the summation of the arrows initially shown in the key:

• Fe Fa
  
  Fa Fe

Since the two sets mean the same thing, we did not write both out, but the idea is there

Please let me know if that makes sense. Thanks!

[momgoingbacktoschool]

Hi Mom,

Thanks for the question! Remember, the double-not arrows are summations of relationships. So, this diagram:

• Fe Fa

Is actually the summation of the arrows initially shown in the key:

• Fe Fa
  
  Fa Fe

Since the two sets mean the same thing, we did not write both out, but the idea is there

Please let me know if that makes sense. Thanks!

Yes, thank you!