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Thread: Logic exercises

  1. #1
    Super Member maxpancho's Avatar
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    Logic exercises




    1. Neither X nor Y, or both X and Y.
    2. X and Y are equally false.
    3. Yes
    4. No
    5. Yes
    6. Yes

    Are these correct answer, could someone check?
    Thank you.
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  2. #2
    MHF Contributor

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    Re: Logic exercises

    You have almost all of those wrong. Have you really studied this at all?

    The original form of the first is \left( {X \wedge \neg Y} \right) \vee \left( {\neg X \wedge Y} \right).
    i.e. "Exactly one is true". Now negate that.
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  3. #3
    Super Member maxpancho's Avatar
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    Re: Logic exercises

    No, it's an appendix in a book, where these questions are thrown at you after about 5 pages of some superficial info. I guess it's more like a test then; maybe I'm just too bad at it. I guess I'd better pick up a book on logic then. Thanks for pointing out the mistakes.
    Last edited by maxpancho; Mar 29th 2015 at 07:29 AM.
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  4. #4
    Super Member maxpancho's Avatar
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    Re: Logic exercises

    Plato, so what do we get here? In the first?

    Is it just: $\neg(X \wedge \neg Y) \vee \neg(\neg X \wedge Y)$ or $(\neg X \wedge Y) \vee ( X \wedge \neg Y)$, which is the same as the original statement?
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  5. #5
    Super Member maxpancho's Avatar
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    Re: Logic exercises

    And what about these answers?

    2. X and Y are equally false.
    3. No
    4. No
    5. Yes
    6. No
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  6. #6
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    Re: Logic exercises

    Quote Originally Posted by maxpancho View Post
    Plato, so what do we get here? In the first?

    Is it just: $\neg(X \wedge \neg Y) \vee \neg(\neg X \wedge Y)$ or $(\neg X \wedge Y) \vee ( X \wedge \neg Y)$, which is the same as the original statement?
    If you are confused, then please study this.
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  7. #7
    Super Member maxpancho's Avatar
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    Re: Logic exercises

    Ah okay. So we just invert the truth table and get the result. So in this case it turns out that by negating we get the truth table of iff.

    Also, I can only write it like this $\neg((X \wedge \neg Y) \vee (\neg X \wedge Y))$ and not like I did.

    So 1 and 2 are invert of each other pretty much.
    Last edited by maxpancho; Apr 19th 2015 at 12:26 PM.
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  8. #8
    Super Member maxpancho's Avatar
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    Re: Logic exercises

    And I actually I just checked on wolfram (hadn't known I could have looked up truth tables there) it turns out that in the original post the answer to 3-6 were correct?

    Spoiler:

    3. https://www.wolframalpha.com/input/?...plies+not+y%29
    4. https://www.wolframalpha.com/input/?...plies+not+x%29
    5. https://www.wolframalpha.com/input/?...+%28y+iff+z%29
    6. https://www.wolframalpha.com/input/?...z+implies+x%29

    Original answers:
    3. Yes
    4. No
    5. Yes
    6. Yes

    Do I understand correctly that "logically equivalent" here means "iff"? Because, that's what I was answering.
    Last edited by maxpancho; Apr 19th 2015 at 12:35 PM.
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