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Failing Sufficient and Necessary

Omed_OvOOmed_OvO Alum Member
in General 158 karma
Hi folks,

I'm currently on the section of our syllabus that requires us to draw valid conclusions. I can't seem to figure out why/when to fail sufficient and necessary conditions.

(i.e.) Y-->G-->H-->B
/H

Can someone help explain?! Much appreciated!
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  • Accounts PlayableAccounts Playable Live Sage ⭐
    3107 karma
    In a LR question, the fact pattern might give you a conditional relationship, and tell you that something isn't the case. This usually signals that you need to negate some stuff in your lawgic chain and see what triggers.

    In a LG, the rules may give you a conditional relationship (like an In/Out game), and a question stem might tell you R is in, so what must be true. Placing R in will probably trigger things in the lawgic chain.

    In your example, you are given two premises:
    1.) A relationship: Y--->G--->H--->B
    2.) A fact: Not H

    What conclusions can you draw?
    Not H is a necessary condition for G AND it is a necessary condition for Y (since Y implies H). So, you are failing a necessary (required) condition for G and Y. Thus, you must have Not G and Not Y.

    H is a sufficient condition for B. Failing the sufficient condition doesn't trigger anything because there might be other ways B can trigger.

    Here's a pretty helpful lesson to practice: https://7sage.com/lesson/conditional-rules-in-games-drill-flashcards
  • Omed_OvOOmed_OvO Alum Member
    158 karma
    Fantastic! Really helped! Thanks!
  • apwilliamsapwilliams Alum Member
    26 karma
    I wrote a rule cheat sheet for me to practice with:

    1. Sufficient Satisfied- Follow arrow forward
    2. Opposite Sufficient- Arrow to the right falls away

    3. Necessary Satisfied- Arrow to the left falls away
    4. Opposite Necessary- Follow contrapositive back
  • shizuokatwin379shizuokatwin379 Alum Member
    edited February 2016 95 karma
    Right (premises) move right.

    Wrong (premises), everything left is wrong.

    What this means if is something is right everything to the right of it has to be right. Right here means it matches your chain. A not x, for example, would be right by being not x.

    If something is wrong, everything to the left (everything left) is also wrong. Meaning it all has to be reversed. (Not x becomes x, y becomes not y)
  • MrSamIamMrSamIam Inactive ⭐
    2086 karma
    When you fail the sufficient, the rule falls away. In other words, assuming that just the sufficient was failed, everything to the right is now "free" - no longer bound by any rules.
    When you fail the necessary, the sufficient must also be failed (think about it: The thing that is necessary/required for the sufficient to occur is no longer present...so, you can't have the sufficient).

    With longer conditional chains (3+ variables) some of the variables will act as sufficient conditions to 1 or more variables, but will also be necessary conditions to 1 or more variables.

    Y--->G--->H--->B

    So, let's look at H.
    H is sufficient for B. It is to the left of B. So are G and Y, but forget about those for now.
    But wait, H is also necessary. Not for B, but for G. And since it's necessary for G, which is necessary for Y, it is also necessary for Y.

    Here are the 2 possible outcomes if H is either failed or met.

    If you're told that H is present. Then the sufficient for B has been met, and B (the necessary) must also be present.

    If you're told "No H." Then the necessary condition for G is no longer present. So, G cannot be present. But wait, again, G is necessary for Y. So, since "No H" screwed over G, it also screws over Y (in other words, no H = No G. No G = No Y).
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