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Math Help - Logic translation

  1. #1
    Super Member angel.white's Avatar
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    Logic translation

    I got this question wrong on my test, and I just can't understand why. I was supposed to translate this sentence into sentential logic. (I posted it in discrete math b/c there is no section for logic, but logic is covered in discrete math)

    Sentence:
    If my plans work out, then even though I got a D on the first test I will go into the final with a good average. (use P,D,G as propositions)

    My translation:
    P\to G
    D

    Expected translation:
    P\to (D &  G)

    On the answer key, my professor added a note which said "even though" = "and"

    I guess when I read it, "even though I got a D" means that I already got a D, so getting a D must be true regardless of what my plans are. So in my interpretation, D is always true (because it already happened). In his interpretation, D is true if P is true, meaning both P and D could be false.

    I want to go argue the point with him, but I figured I'd see what you guys think first, b/c you guys are considerably more educated than I am. Also, if you disagree with me, can you post an easy to understand reason why, and if you do agree with me, can you suggest a method of validating my interpretation.
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  2. #2
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    Quote Originally Posted by angel.white View Post
    Sentence:
    If my plans work out, then even though I got a D on the first test I will go into the final with a good average. (use P,D,G as propositions)

    Expected translation:
    P\to (D &  G)
    I agree with your instructor.
    I read it as: "If my plans work out, then even with a D I will go into the final with a good average."
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  3. #3
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    Quote Originally Posted by angel.white View Post
    I got this question wrong on my test, and I just can't understand why. I was supposed to translate this sentence into sentential logic. (I posted it in discrete math b/c there is no section for logic, but logic is covered in discrete math)

    Sentence:
    If my plans work out, then even though I got a D on the first test I will go into the final with a good average. (use P,D,G as propositions)

    My translation:
    P\to G
    D

    Expected translation:
    P\to (D &  G)

    On the answer key, my professor added a note which said "even though" = "and"

    I guess when I read it, "even though I got a D" means that I already got a D, so getting a D must be true regardless of what my plans are. So in my interpretation, D is always true (because it already happened). In his interpretation, D is true if P is true, meaning both P and D could be false.

    I want to go argue the point with him, but I figured I'd see what you guys think first, b/c you guys are considerably more educated than I am. Also, if you disagree with me, can you post an easy to understand reason why, and if you do agree with me, can you suggest a method of validating my interpretation.
    You have a case. "Even though" does mean and, but I think your professor is attaching it to the wrong clause. The sentence should read better:

    Even though I got a D, if my plans work out, then I will go into the final with a good average. It's D & (P -> G).

    The statement as read should obviously be false if you didn't get a D on first test, but if your professor's result is correct, then the statement would hold true in a world where your plans didn't work out, you passed the test, and went into the final with a poor average (because False->(False & False) is true).. But in our better answer, False & (False->False) = False & True = False, which is how it should be under those circumstances.

    Consider a statement with the same structure whose meanings are even more obvious: If I can find a partner, even though it's raining, I am going to play tennis. It is absurd to interpret this as anything other than It's raining AND if I can find a parter, I'm going to play tennis., not If I can find a partner, then it is raining and I'll play tennis. In the latter case, the statement would be true in some conditions even if it wasn't raining.
    Go get your points.
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