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UnkleRhaukus
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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) \[\neg\neg \psi\quad\longrightarrow\quad \psi\]
UnkleRhaukus
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any mistakes?
hartnn
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(c) ?
UnkleRhaukus
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sure?
hartnn
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its correct.
except for imaginary x
UnkleRhaukus
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so this is a more gerneral answer to c)\[\neg(x^2 > 0)\quad\longrightarrow\quad x\in\Im\]?
hartnn
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yup.
but if it is mentioned that x is real, then x=0.
else x belongs to imaginary.
hartnn
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sorry, x belongs to imaginary or x=0
UnkleRhaukus
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\[\longrightarrow \Re(x)=0\]
UnkleRhaukus
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im a bit confused, what if x is complex
hartnn
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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
UnkleRhaukus
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im not sure
UnkleRhaukus
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maybe all i can do is this \[\neg(x^2 > 0)\quad\longrightarrow\quad x^2\leq0\]
UnkleRhaukus
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@AccessDenied
UnkleRhaukus
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what is the best answer for part (c)
Jemurray3
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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.
UnkleRhaukus
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so i should leave it as i had it at the top of the page then ,
Jemurray3
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I would say yes.
UnkleRhaukus
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thanks