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Math Help - logic related question ...

  1. #31
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    Re: logic related question ...

    The first (left) part of Law 3 is the same as the end of Step 4, and the second (right) part of Step 3 is the same as the beginning of step 4. So, in Step 4, Law 3 is applied right-to-left.
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  2. #32
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    Re: logic related question ...

    Quote Originally Posted by emakarov View Post
    The first (left) part of Law 3 is the same as the end of Step 4, and the second (right) part of Step 3 is the same as the beginning of step 4. So, in Step 4, Law 3 is applied right-to-left.
    Ok so we are allowed to repeat the same step multiple times ...

    So now we have:

    Step 1: p ∨ q = Law 3
    Step 2: q ∨p = ...
    Step 3: (q) ∨ p = Law 2
    Step 4: q ⇒ p = Law 3

    So now we only need to find out Step 2 ...

    Step 2: q ∨p = ...

    and it looks like that Law 3 is used again here ... is that possible?
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  3. #33
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    Re: logic related question ...

    Iwan, what is the name of the book you are reading in connection with logic
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  4. #34
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    Re: logic related question ...

    Iwan, what is the name of the book you are reading in connection with logic
    I am just using resources online ...
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  5. #35
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    Re: logic related question ...

    That is your problem.

    Unless you get a whole book and start from the beginning and make sure you understand each and every chapter ,then you might have a chance to realise what you are doing and the meaning behind it .

    Taking for example the classic book "introduction to logic" by Irving Copi you will find that the problem you are trying to solve is in chapter 9.

    How about the 8 chapters before??
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  6. #36
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    Re: logic related question ...

    I exactly know what you mean ... and I fully agree ...
    But the problem is time here :-) ... so I am trying to make the best of it ... and some things are easier to understand then others ...
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  7. #37
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    Re: logic related question ...

    One of my instructors used to say, "It is better not to finish anything than not to understand anything."
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  8. #38
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    Re: logic related question ...

    Back on topic :-)

    So far we still have:

    Step 1: p ∨ q = Law 3
    Step 2: q ∨ p = ...
    Step 3: (q) ∨ p = Law 2
    Step 4: q ⇒ p = ...

    The Laws that we can choose from:

    Law 1: (a ∨ b) ⇔ (b ∨ a)
    (commutativity of ∨)

    Law 2: (a) ⇔ a
    (law of negation)

    Law 3: (a ⇒ b) ⇔ (a ∨ b)
    (law of implication)

    Law 4: (a ⇔ b) ⇔ ((a ⇒ b) ∧ (b ⇒ a))
    (law of equivalence)

    Explanation of the steps:

    So with step 1 it was obvious that Step 1 (p ∨ q) belonged to Law 3 (a ⇒ b) ⇔ (a ∨ b)
    Because we see that "p" corrosponds with "a" and "q" corrosponds with "b"

    And with step 3 ( (q) ∨ p ) it was also clear that law 2 (a ⇒ b) ⇔ (a ∨ b) is the lucky one.
    Becasue when we replace the "a" with "q" and "b" with "p" the result will be (q ⇒ p) ⇔ (q ∨ p)

    So the only steps we have left to solve is Step 2 and Step 4...
    And the Laws that we have not used yet are Law 1 and Law 4

    This is correct until now right?
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  9. #39
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    Re: logic related question ...

    Yes, and I also wrote which laws are used in steps 2 and 4 in my previous posts.
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  10. #40
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    Re: logic related question ...

    Quote Originally Posted by emakarov View Post
    Yes, and I also wrote which laws are used in steps 2 and 4 in my previous posts.
    Post #31 you indeed said:
    Step 4, Law 3 is applied right-to-left.

    For Step 2 I can not find anything ...
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  11. #41
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    Re: logic related question ...

    See post #17, as I also wrote in the private message.
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  12. #42
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    Re: logic related question ...

    Quote Originally Posted by emakarov View Post
    See post #17, as I also wrote in the private message.
    I see now ...

    Step 1 = Law 3
    Step 2 = Law 1
    Step 3 = Law 2
    Step 4 = Law 3

    You know what my big problem is ...
    That is that I was in the understanding that we should use all given laws only 1 time ... and now that Law3 is used twice and Law 4 is not used at all I realise that this is not needed...
    We just use the Laws acording to needs ... and this can well be that a Law is used multiple times...

    Thanks for your patience with this one :-)
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