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UnkleRhaukus

  • 2 years ago

Negation

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  1. UnkleRhaukus
    • 2 years ago
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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. UnkleRhaukus
    • 2 years ago
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    any mistakes?

  3. hartnn
    • 2 years ago
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    (c) ?

  4. UnkleRhaukus
    • 2 years ago
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    sure?

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

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

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

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

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

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

  11. hartnn
    • 2 years ago
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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

  12. UnkleRhaukus
    • 2 years ago
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    im not sure

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

  14. UnkleRhaukus
    • 2 years ago
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    @AccessDenied

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

  16. Jemurray3
    • 2 years ago
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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.

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

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

  19. UnkleRhaukus
    • 2 years ago
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    thanks

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