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Bi-conditional vs Not both rule confusion

gparmar92gparmar92 Alum Member
edited November 2017 in Logic Games 153 karma

Hi I was just wondering if someone could clear this up for me, because this confusion cost me quite a few points on in-out games, by making me hesitate

Example rules:

(1) K <----> /M
(2) K ----> /M

(1) would be a bi-conditional (always apart never together) and (2) would be a typical not-both rule.

My confusion centers around what would happen if given the premise K is out ( /K )...

The second rule would be considered irrelevant (sufficient failed), and "M" is free to float (correct me on this if I'm wrong); but would the first rule get "triggered" (meaning M would be in) because its an always apart never together bi-conditional?OR would the bi-conditional also be considered irrelevant because the sufficient condition is also getting failed in (1)? I'm hoping somebody could explain the logic behind how/what happens. I mean in the explanation videos JY usually splits the master game board if provided with a rule like (1) where K is in and M is out on one, and vice versa on the other, so you never have to really deal with the situation I've presented, since its already represented.

I guess I'm just curious lol

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Comments

  • BinghamtonDaveBinghamtonDave Alum Member ⭐ 🍌🍌
    8716 karma

    K<---->M is a biconditional. It is read both ways and we can also read the contrapositives. This is designed to cover every possible world in the in and out game. So unpacking the biconditional reading the arrow forward we have:
    K<--->M

    If K is in then M is out
    Contrapositive of that statement is
    If M is in then K is out

    Now we read the statement backwards:
    K<---->M
    If M is out then K is in
    Contrapositive of that is:
    If K is out then M is in

    The purpose of mastery over this concept for in and out games is that we have every single base covered via a sufficient condition:
    What happens when M is in?
    What happens when M is out?
    What happens when K is in?
    What happens when K is out?
    By "what happens" I mean what is triggered/what is necessary

    This works out so neatly for in and out games because we only have (for the most part) two categories.

    The Not both rule you have written above as number 2 is often far more restrictive in what we can draw from it. I think of this rule as it relates to grouping games: if you have Three groups and K and M cannot be together, but if K is in group 1, the only thing we can draw from that is that M must be in group 2 or 3 (assuming we have to use all the piece.) A way I have of looking at a not both rule for grouping games is I tell myself "If I see a K, I better not see an M in that group" For in and out games, because we are playing such a restrictive in/out game board, this simple not both iteration might cause some confusion, because as you point out: we might fail the sufficient condition and (wrongly) assume that the rule falls apart on an in and out game.

    Now, there is a small exception in my estimation on in and out games where the rule you have listed as number 2 might provide us with a greater ability to manipulate the game pieces: that in which we have an in and out game with sub categories. Meaning from a group of 7, we are choosing two groups of 3 with 1 out for instance. In this case, the biconditional does not hold the same way it does for traditional in and out games.

    I hope the above helps
    David

  • GrecoRomanGrecoRoman Alum Member
    140 karma

    Each term in a biconditional relationship has a necessary and sufficient condition, so they trigger no matter what. K<------->/M breaks down to:

    K--------->/M and /M-------->K, with contrapositives M------->/K and /K---------->M

    So it doesn't matter if you have K or /K, M or /M, each one is sufficient to trigger it's necessary condition.

  • gparmar92gparmar92 Alum Member
    153 karma

    @BinghamtonDave said:
    K<---->M is a biconditional. It is read both ways and we can also read the contrapositives. This is designed to cover every possible world in the in and out game. So unpacking the biconditional reading the arrow forward we have:
    K<--->M

    If K is in then M is out
    Contrapositive of that statement is
    If M is in then K is out

    Now we read the statement backwards:
    K<---->M
    If M is out then K is in
    Contrapositive of that is:
    If K is out then M is in

    The purpose of mastery over this concept for in and out games is that we have every single base covered via a sufficient condition:
    What happens when M is in?
    What happens when M is out?
    What happens when K is in?
    What happens when K is out?
    By "what happens" I mean what is triggered/what is necessary

    This works out so neatly for in and out games because we only have (for the most part) two categories.

    The Not both rule you have written above as number 2 is often far more restrictive in what we can draw from it. I think of this rule as it relates to grouping games: if you have Three groups and K and M cannot be together, but if K is in group 1, the only thing we can draw from that is that M must be in group 2 or 3 (assuming we have to use all the piece.) A way I have of looking at a not both rule for grouping games is I tell myself "If I see a K, I better not see an M in that group" For in and out games, because we are playing such a restrictive in/out game board, this simple not both iteration might cause some confusion, because as you point out: we might fail the sufficient condition and (wrongly) assume that the rule falls apart on an in and out game.

    Now, there is a small exception in my estimation on in and out games where the rule you have listed as number 2 might provide us with a greater ability to manipulate the game pieces: that in which we have an in and out game with sub categories. Meaning from a group of 7, we are choosing two groups of 3 with 1 out for instance. In this case, the biconditional does not hold the same way it does for traditional in and out games.

    I hope the above helps
    David

    The above helps greatly, thank you so much for your detailed explanation. I really appreciate it, and (as a Canadian lol) sorry I didn't take a look back this thread until now, I got busy wtih things. Nonetheless again thanks for such a detailed explanation. cheers!

  • gparmar92gparmar92 Alum Member
    153 karma

    @"work all week" said:
    Each term in a biconditional relationship has a necessary and sufficient condition, so they trigger no matter what. K<------->/M breaks down to:

    K--------->/M and /M-------->K, with contrapositives M------->/K and /K---------->M

    So it doesn't matter if you have K or /K, M or /M, each one is sufficient to trigger it's necessary condition.

    This makes a lot of sense. I can see why if you get an always apart never together rule why you would split an in/out game board into 2 (one where K is in M is out, and the other where K is out and M is in). It's because of the relationships that a bi-conditional entails/contains that you detailed above. Thanks a lot!

  • ChaudhrySChaudhryS Free Trial Member
    61 karma

    @BinghamtonDave said:
    K<---->M is a biconditional. It is read both ways and we can also read the contrapositives. This is designed to cover every possible world in the in and out game. So unpacking the biconditional reading the arrow forward we have:
    K<--->M

    If K is in then M is out
    Contrapositive of that statement is
    If M is in then K is out

    Now we read the statement backwards:
    K<---->M
    If M is out then K is in
    Contrapositive of that is:
    If K is out then M is in

    The purpose of mastery over this concept for in and out games is that we have every single base covered via a sufficient condition:
    What happens when M is in?
    What happens when M is out?
    What happens when K is in?
    What happens when K is out?
    By "what happens" I mean what is triggered/what is necessary

    This works out so neatly for in and out games because we only have (for the most part) two categories.

    The Not both rule you have written above as number 2 is often far more restrictive in what we can draw from it. I think of this rule as it relates to grouping games: if you have Three groups and K and M cannot be together, but if K is in group 1, the only thing we can draw from that is that M must be in group 2 or 3 (assuming we have to use all the piece.) A way I have of looking at a not both rule for grouping games is I tell myself "If I see a K, I better not see an M in that group" For in and out games, because we are playing such a restrictive in/out game board, this simple not both iteration might cause some confusion, because as you point out: we might fail the sufficient condition and (wrongly) assume that the rule falls apart on an in and out game.

    Now, there is a small exception in my estimation on in and out games where the rule you have listed as number 2 might provide us with a greater ability to manipulate the game pieces: that in which we have an in and out game with sub categories. Meaning from a group of 7, we are choosing two groups of 3 with 1 out for instance. In this case, the biconditional does not hold the same way it does for traditional in and out games.

    I hope the above helps
    David

    This. Needs. To. Be. Published. Thank YOU!

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