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UnkleRhaukus Group Title

Negation

  • 2 years ago
  • 2 years ago

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  1. UnkleRhaukus Group Title
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    (a) \[\neg(\pi>3.2)\quad\longrightarrow\quad\pi\leq 3.2\](b) \[\neg (x < 0)\quad\longrightarrow\quad x\geq 0\](c) \[\neg(x^2 > 0)\quad\longrightarrow\quad x=0\] (d) \[\neg(x = 1)\quad\longrightarrow\quad x\neq 1\](e) \[\neg\neg \psi\quad\longrightarrow\quad \psi\]

    • 2 years ago
  2. UnkleRhaukus Group Title
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    any mistakes?

    • 2 years ago
  3. hartnn Group Title
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    (c) ?

    • 2 years ago
  4. UnkleRhaukus Group Title
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    sure?

    • 2 years ago
  5. hartnn Group Title
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    its correct. except for imaginary x

    • 2 years ago
  6. UnkleRhaukus Group Title
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    so this is a more gerneral answer to c)\[\neg(x^2 > 0)\quad\longrightarrow\quad x\in\Im\]?

    • 2 years ago
  7. hartnn Group Title
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    yup. but if it is mentioned that x is real, then x=0. else x belongs to imaginary.

    • 2 years ago
  8. hartnn Group Title
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    sorry, x belongs to imaginary or x=0

    • 2 years ago
  9. UnkleRhaukus Group Title
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    \[\longrightarrow \Re(x)=0\]

    • 2 years ago
  10. UnkleRhaukus Group Title
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    im a bit confused, what if x is complex

    • 2 years ago
  11. hartnn Group Title
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    but, if x is complex then u x^2 can be positive. yes,even i was thinking that. better assume x as real then x=0

    • 2 years ago
  12. UnkleRhaukus Group Title
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    im not sure

    • 2 years ago
  13. UnkleRhaukus Group Title
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    maybe all i can do is this \[\neg(x^2 > 0)\quad\longrightarrow\quad x^2\leq0\]

    • 2 years ago
  14. UnkleRhaukus Group Title
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    @AccessDenied

    • 2 years ago
  15. UnkleRhaukus Group Title
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    what is the best answer for part (c)

    • 2 years ago
  16. Jemurray3 Group Title
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    Typically when you're talking about statements of logic you work in real numbers for simplicity just to get the ideas of negation and implication and all that stuff down. I would mark (c) as correct. Furthermore, since complex numbers are not ordered, the symbols don't make sense for complex numbers, lending credence to the assumption that the quantities in question are real.

    • 2 years ago
  17. UnkleRhaukus Group Title
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    so i should leave it as i had it at the top of the page then ,

    • 2 years ago
  18. Jemurray3 Group Title
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    I would say yes.

    • 2 years ago
  19. UnkleRhaukus Group Title
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    thanks

    • 2 years ago
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