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UnkleRhaukus

  • 3 years ago

\[\begin{array}{ccccc}\phi & \neg \phi & \psi & \phi \Rightarrow \psi & \neg \phi \vee \psi \\ \hline \\T&F&T &T&?\\T&F&F&F&?\\F&T&T&T&?\\F&T&F&T&?\end{array}\]

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  1. RedPrince
    • 3 years ago
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    T F T F

  2. UnkleRhaukus
    • 3 years ago
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    i think i made a mistake in the table already

  3. UnkleRhaukus
    • 3 years ago
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    sorry about that

  4. RedPrince
    • 3 years ago
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    ¬ϕ∨ψ means if either ¬ϕ is true or either ψ is true or both are true then the answer is true otherwise it is false ¬ϕ is false but ψ is true so the answer is true, and so on

  5. RedPrince
    • 3 years ago
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    post your question again and right!!

  6. UnkleRhaukus
    • 3 years ago
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    \[\begin{array}{ccccc}\phi & \neg \phi & \psi & \phi \Rightarrow \psi & \neg \phi \vee \psi \\ \hline \\T&F&T &T&T\\T&F&F&F&F\\F&T&T&T&T\\F&T&F&T&T\end{array}\] is that right?

  7. UnkleRhaukus
    • 3 years ago
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    it makes sense now, your answer form before , was right for the table i posted originally

  8. RedPrince
    • 3 years ago
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    last one is wrong one of ψ and ¬ϕ is true, so how can it be true.....!!! check this! http://www.hermit.cc/teach/ho/dbms/optable.htm

  9. UnkleRhaukus
    • 3 years ago
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    ?

  10. swissgirl
    • 3 years ago
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    hmmm It seems to be that you are correct Unkle

  11. swissgirl
    • 3 years ago
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    me*

  12. swissgirl
    • 3 years ago
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    I cant seem to find where you went wrong. Everything seems correct

  13. UnkleRhaukus
    • 3 years ago
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    cool, what about this one \[\begin{array}{cccccc}\phi & \psi & \neg\psi & \phi \Rightarrow \psi & \phi \not\Rightarrow \psi &\psi\wedge\neg\psi\\ \hline \\T&T &F&T&\\T&F&T&F&\\F&T&F&T&\\F&F&T&T& \end{array}\]

  14. swissgirl
    • 3 years ago
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    The last column is obv false

  15. swissgirl
    • 3 years ago
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    I am not sure what that sign is of the second to last column

  16. anonymous
    • 3 years ago
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    You were correct above, proving that the statements are logically equivalent

  17. UnkleRhaukus
    • 3 years ago
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    |dw:1348840677936:dw|

  18. UnkleRhaukus
    • 3 years ago
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    phi does not imply psi

  19. swissgirl
    • 3 years ago
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    hmmm Y have I never come across that one????? Ok Let me go get my book and see

  20. swissgirl
    • 3 years ago
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    Well isnt that then the same as ~(P->Q) I mean it should just be the opposite of the column before

  21. UnkleRhaukus
    • 3 years ago
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    \[\begin{array}{cccccc}\phi & \psi & \neg\psi & \phi \Rightarrow \psi & \phi \nRightarrow \psi &\phi\wedge\neg\psi\\ \hline \\T&T &F&T&\\T&F&T&F&\\F&T&F&T&\\F&F&T&T& \end{array}\]

  22. swissgirl
    • 3 years ago
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    waitttt we didnt finish the previous one lol

  23. UnkleRhaukus
    • 3 years ago
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    is \[\phi\nRightarrow\psi\] the same as \[\neg\phi\Rightarrow\psi\]?

  24. swissgirl
    • 3 years ago
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    Noooo IN brackets

  25. swissgirl
    • 3 years ago
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    \(\neg(\phi\Rightarrow\psi)\)

  26. UnkleRhaukus
    • 3 years ago
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    hmm,

  27. swissgirl
    • 3 years ago
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    cuz idk I remember doing this stuff and we never came across that symbol

  28. UnkleRhaukus
    • 3 years ago
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    ok so you were right\[\phi\nRightarrow\psi\]\[\downarrow\]\[\neg(\phi\Rightarrow\psi)\]\[\downarrow\] opposite to the previous column,

  29. swissgirl
    • 3 years ago
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    yup

  30. swissgirl
    • 3 years ago
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    The last column is F T F F

  31. UnkleRhaukus
    • 3 years ago
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    \[\begin{array}{cccccc}\phi & \psi & \neg\psi & \phi \Rightarrow \psi & \phi \nRightarrow \psi &\phi\wedge\neg\psi\\ \hline \\T&T &F&T&F&F\\T&F&T&F&T&T\\F&T&F&T&F&F\\F&F&T&T&F&F \end{array}\]

  32. swissgirl
    • 3 years ago
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    Ya that is correct

  33. UnkleRhaukus
    • 3 years ago
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    how did you get the last column ?

  34. swissgirl
    • 3 years ago
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    Ok well that is known as the and connective And the rule there is that a true with False=False A false with a fasle is false and a true with a true =true And it should make sense logically in your brain FALSE AND FALSE=FALSE TRUE AND FALSE cant be true it must be FALSE TRUE AND TRUE is obv TRUE

  35. UnkleRhaukus
    • 3 years ago
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    i dont think i understand the difference between ¬φ ∨ ψ these φ ∨ ¬ψ

  36. swissgirl
    • 3 years ago
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    Ok well firstly the connective is the or connective and its always true except when both compartments are false So TRUE OR TRUE=TRUE TRUE OR FALSE=TRUE Lets take the sentence I went to bed early or i went to bed on time Its true statement even though one half of the sentence contradicts the other FALSE OR FALSE+FALSE

  37. swissgirl
    • 3 years ago
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    FALSE OR FALSE=FALSE

  38. swissgirl
    • 3 years ago
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    The only difference is which column you will use.

  39. swissgirl
    • 3 years ago
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    Like one phi is negative and the other psi is negative

  40. swissgirl
    • 3 years ago
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    Well basically if you dont understand the difference then you are basically not following how truth tables are formed

  41. swissgirl
    • 3 years ago
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    ok lets make a truth table.

  42. swissgirl
    • 3 years ago
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    |dw:1348842795418:dw|

  43. swissgirl
    • 3 years ago
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    This drawing board was def testing my patience

  44. swissgirl
    • 3 years ago
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    the way i figured out the last 2 columns was look at the appropriate 2 columns and decide if it would be true or false

  45. swissgirl
    • 3 years ago
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    Do you follow?

  46. UnkleRhaukus
    • 3 years ago
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    YES that table makes sense now thankyou ! @swissgirl

  47. swissgirl
    • 3 years ago
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    lol I hope so. Its kinda hard to explain but if you start from the wayyyyyy begginning then like once you get it its simple

  48. UnkleRhaukus
    • 3 years ago
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    i guess we can conclude that \[\phi\Rightarrow\psi\qquad\leftrightarrow\qquad\neg\phi\vee\psi\] and \[\phi\nRightarrow\psi\qquad\leftrightarrow\qquad\phi\vee\neg\psi\]

  49. swissgirl
    • 3 years ago
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    I dont like the second part of your conclusion Are you sure that it is correct?

  50. UnkleRhaukus
    • 3 years ago
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    oh yeah i got that a wrong

  51. UnkleRhaukus
    • 3 years ago
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    \[\phi\nRightarrow\psi\qquad\leftrightarrow\qquad\phi\wedge\neg\psi\]

  52. swissgirl
    • 3 years ago
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    YAAA thats correct

  53. UnkleRhaukus
    • 3 years ago
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    thanks again,

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