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Conditional logic help.

LsatbreakingnewsLsatbreakingnews Alum Member
edited September 2016 in General 392 karma
Hi guys, I was helping my friend out with conditional logic today because I thought I had a grasp on the material but it turns out I dont....
So there was a statement from one of his textbooks he asked me to help him out with and I got it wrong.

Dmitry might play volleyball or squash, but he cant play both.
(edit meant to say might play not, might can)

So I thought great this is a bi-conditional because I see or but not both.
So I made it into: (~V <---> S) & (V <---> ~S),
But it turns out in his textbook the answer was (S -> ~V) & (V -> ~S).
So is this a different way of showing the same relationship, if so do you prefer one method over the other?
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Comments

  • MrSamIamMrSamIam Inactive ⭐
    2086 karma
    Are you sure the sentence is, "Dmitry might can volleyball or squash, but he cant play both"?

    In any case, what you have there is an exclusive "or." In other words, one of the two will happen, and when it does, the other will be precluded. That is why they diagrammed it the way they did in the textbook.

    In all honesty, I would have diagrammed it as a bi-conditional just like you did, simply because of the "not both" statement. But, I can see why they didn't (when you negate their diagram, it ends up looking like a bi-conditional).
  • quinnxzhangquinnxzhang Member
    edited September 2016 611 karma
    @Euthyphro said:
    (~V <---> S) & (V <---> ~S)
    This is redundant. The two biconditionals in your conjunct are equivalent.
    @Euthyphro said:
    So is this a different way of showing the same relationship, if so do you prefer one method over the other?
    No, your translation is not equivalent to textbook's and does not say the same thing. Presumably, the textbook is zoning in on the "might" keyword. They're interpreting the sentence to say that Dmitry doesn't have to play either; he just can't play both. Your translation, on the other hand, says the Dmitry must play one and he can't play both.

    It's worth noting that their translation
    @Euthyphro said:
    (S -> ~V) & (V -> ~S)
    is also redundant. Both conditionals in the conjunct are equivalent (they're contrapositives of each other).

    I think this is also a case where trying to gerrymander everything into conditionals can be confusing. We think naturally in ANDs and ORs, so converting to ANDs and ORs may be more intuitive for you.

    Recall that 'P -> Q' is equivalent to '~P or Q'. So, converting their translation, we have '~S or ~V'. Converting your translation, we have '(S or V) and ~(S and V)'.
  • desire2learndesire2learn Member
    1171 karma
    I agree with @"quinnxzhang" on this one. You are missing the "might" aspect of the statement. It is an odd way of having a not both statement because you can have one, the other, or neither. Thus the correct translation would be V-->/S because you can have V "in" with S "out", S "in" with V "out", or V and S both "out" (Dmitry doesn't play either one).
  • MrSamIamMrSamIam Inactive ⭐
    2086 karma
    @quinnxzhang said:
    No, your translation is not equivalent to textbook's and does not say the same thing. Presumably, the textbook is zoning in on the "might" keyword. They're interpreting the sentence to say that Dmitry doesn't have to play either; he just can't play both. Your translation, on the other hand, says the Dmitry must play one and he can't play both.
    Good catch, ignore my above statement about them being equivalent. I completely missed the "might" - which, as mentioned allows for a "neither" possibility.
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