Question

Negation

Answer 1

(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) \[\neg\neg \psi\quad\longrightarrow\quad \psi\]

Answer 2

any mistakes?

Answer 3

(c) ?

Answer 4

sure?

Answer 5

its correct.
except for imaginary x

Answer 6

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

Answer 7

yup.
but if it is mentioned that x is real, then x=0.
else x belongs to imaginary.

Answer 8

sorry, x belongs to imaginary or x=0

Answer 9

\[\longrightarrow \Re(x)=0\]

Answer 10

im a bit confused, what if x is complex

Answer 11

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

Answer 12

im not sure

Answer 13

maybe all i can do is this \[\neg(x^2 > 0)\quad\longrightarrow\quad x^2\leq0\]

Answer 14

@AccessDenied

Answer 15

what is the best answer for part (c)

Answer 16

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.

Answer 17

so i should leave it as i had it at the top of the page then ,

Answer 18

I would say yes.

Answer 19

thanks