Question

Simplify the following symbolic statement as much as you can, leaving your answer in a standard symbolic form
\[(x>3)\vee(x^2>9)\quad\longrightarrow\quad (x>3)\vee\left((x>3) \vee (x<-3)\right)\]
\[\qquad\qquad\qquad\longrightarrow\quad (x>3)\vee (x<-3)\]

which is simpler? \[(x>3)\vee (x<-3)\quad\longleftrightarrow \quad (x^2>9)\]

Answer 1

RHS maybe?

Answer 2

my argument for the LSH is that x is isolated

Answer 3

but theres 2 of them over there :)

Answer 4

is there a correct simplification?

Answer 5

yeah , im not convinced on either yet

Answer 6

why not
|x|>3

Answer 7

thatll just cause pandamonia in the streets

Answer 8

i like it anyway @phi, pandemonium or not

Answer 9

are absolute values in standard logic notation ?

Answer 10

but I assume they want (x>3) v (x<-3) in this context

Answer 11

i dunno

Answer 12

@Algebraic! , @Mikael

Answer 13

Well being "logician" for an hour I'd ask:
"Define you criterion of simplicity"

Answer 14

the question give to me is at the top of the page ,

Answer 15

It seems to me that "simplest" in this context means
\[ \Large \color{green}{\text{ Reduced to expressions that do NOT contain}} \\ {\bf \text{any computational operations.}\\ {\text { Only direct descriptions of number sets and their unions}} } \]

Answer 16

E.g. \[ Operator(x) \in A\\ \,\,\,\, \text{Is NOT a simple expression}\\ While \\ x \in A \\ IS\,\,\, a\,simple\,\, expression \]

Answer 17

so LHS is better?

Answer 18

do you know if pandemonium will break loose if i use phi's suggestion?

Answer 19

\[ (x>3)\vee (x<-3)\] Is the proper simplest form.
Pandaemonium unfortunately is what we have already on planet Earth.
We all wish that fairy-tale demons and angels really existed.
Since their existence gives hope to spiritual reality, which most humans yearn to.
Unfortunately I am sceptical as to its existence...

Answer 20

@UnkleRhaukus I've replied to your query

Answer 21

so |x|>3 is no good?

Answer 22

Not good

Answer 23

Simple \[ \neq\] Short

Answer 24

pardon?

Answer 25

The || expression is shortest, but NOT simplest since it contains some operators, and I've already defined that simple-expr.= ONLY SETS

Answer 26

It seems to me that "simplest" in this context means
Reduced to expressions that do NOT containany computational operations. Only direct descriptions of number sets and their unions

Answer 27

so conjunction and disjunction are not computational, therefore are simpler than squaring the variable in this example.

Answer 28

Again TWO (at least TWO) definitions of \[ \Large\color{fuchsia}{'Simple'} \]
If S. is the lowest complexity of mathematical/algebraic/etc computation then |x|< 3 is simplest

2 If [as I think] simplest is the most explicit and basic definition of the set of numbers involved then\[ \text{Set A}\cup\text{Set B} \,\,\,\,\,\,\color{fuchsia}{\text{is THE SIMPLEST expression}} \]

Answer 29

gotcha

Answer 30

If this is a course on Logic/Set theory than My definition is true.

If regular algebra/math ==> |x|<3

Answer 31

@UnkleRhaukus

Answer 32

the question comes to me from a course called
'Introduction to Mathematical Thinking'

Answer 33

@KingGeorge