## UnkleRhaukus 3 years ago Negation

1. UnkleRhaukus

(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

any mistakes?

3. hartnn

(c) ?

4. UnkleRhaukus

sure?

5. hartnn

its correct. except for imaginary x

6. UnkleRhaukus

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

7. hartnn

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

8. hartnn

sorry, x belongs to imaginary or x=0

9. UnkleRhaukus

$\longrightarrow \Re(x)=0$

10. UnkleRhaukus

im a bit confused, what if x is complex

11. hartnn

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

im not sure

13. UnkleRhaukus

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

14. UnkleRhaukus

@AccessDenied

15. UnkleRhaukus

what is the best answer for part (c)

16. Jemurray3

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

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

18. Jemurray3

I would say yes.

19. UnkleRhaukus

thanks