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UnkleRhaukus Group Title

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

  • 2 years ago
  • 2 years ago

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  1. RedPrince Group Title
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    T F T F

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

    • 2 years ago
  3. UnkleRhaukus Group Title
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    sorry about that

    • 2 years ago
  4. RedPrince Group Title
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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

    • 2 years ago
  5. RedPrince Group Title
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    post your question again and right!!

    • 2 years ago
  6. UnkleRhaukus Group Title
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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?

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

    • 2 years ago
  8. RedPrince Group Title
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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

    • 2 years ago
  9. UnkleRhaukus Group Title
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    ?

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

    • 2 years ago
  11. swissgirl Group Title
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    me*

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

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

    • 2 years ago
  14. swissgirl Group Title
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    The last column is obv false

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

    • 2 years ago
  16. satellite73 Group Title
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    You were correct above, proving that the statements are logically equivalent

    • 2 years ago
  17. UnkleRhaukus Group Title
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    |dw:1348840677936:dw|

    • 2 years ago
  18. UnkleRhaukus Group Title
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    phi does not imply psi

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

    • 2 years ago
  20. swissgirl Group Title
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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

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

    • 2 years ago
  22. swissgirl Group Title
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    waitttt we didnt finish the previous one lol

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

    • 2 years ago
  24. swissgirl Group Title
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    Noooo IN brackets

    • 2 years ago
  25. swissgirl Group Title
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    \(\neg(\phi\Rightarrow\psi)\)

    • 2 years ago
  26. UnkleRhaukus Group Title
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    hmm,

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

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

    • 2 years ago
  29. swissgirl Group Title
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    yup

    • 2 years ago
  30. swissgirl Group Title
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    The last column is F T F F

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

    • 2 years ago
  32. swissgirl Group Title
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    Ya that is correct

    • 2 years ago
  33. UnkleRhaukus Group Title
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    how did you get the last column ?

    • 2 years ago
  34. swissgirl Group Title
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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

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

    • 2 years ago
  36. swissgirl Group Title
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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

    • 2 years ago
  37. swissgirl Group Title
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    FALSE OR FALSE=FALSE

    • 2 years ago
  38. swissgirl Group Title
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    The only difference is which column you will use.

    • 2 years ago
  39. swissgirl Group Title
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    Like one phi is negative and the other psi is negative

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

    • 2 years ago
  41. swissgirl Group Title
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    ok lets make a truth table.

    • 2 years ago
  42. swissgirl Group Title
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    |dw:1348842795418:dw|

    • 2 years ago
  43. swissgirl Group Title
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    This drawing board was def testing my patience

    • 2 years ago
  44. swissgirl Group Title
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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

    • 2 years ago
  45. swissgirl Group Title
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    Do you follow?

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

    • 2 years ago
  47. swissgirl Group Title
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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

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

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

    • 2 years ago
  50. UnkleRhaukus Group Title
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    oh yeah i got that a wrong

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

    • 2 years ago
  52. swissgirl Group Title
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    YAAA thats correct

    • 2 years ago
  53. UnkleRhaukus Group Title
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    thanks again,

    • 2 years ago
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