Question

Let x ∈ R. If x^2 - 2x + 2 ≤ 0, then x^3 ≥ 8. Prove that this implication is either true or false. @satellite73 @ganeshie8 @myininaya @UnkleRhaukus @zepdrix @RadEn @robtobey @Luigi0210 @primeralph @shamil98 @Compassionate @nincompoop @Preetha @Euler271 @Kainui @ehuman @wolfe8 @wolf1728 @Yttrium @zpupster @tester97 @emilyhaddad @Lena772 @nikato @sarah786 @Kristen17 @AustinC @kittiwitti1 @adrynicoleb @doggy @lilai3 @thadyoung @lucaz @TheForbiddenFollower @linh412986 @comf@UH60blackhawk @BlackLabel @leozap1 @ComeAlongP0nd @CrayolaCrayon_ @grinnell.12 @David. @lovelycharm @adrynicoleb @Cutefriendz

Answer 1

this is considered a mass tagging and consider this annoying. please refrain from this in the future. thank you.

Answer 2

F -> something

true

Answer 3

Ops dunno ^^

Answer 4

Cellphone.

Answer 5

If x^2 - 2x + 2 ≤ 0, then x^3 ≥ 8.
---------------


that part is false, cuz from the hypothesis, x is real, and we dont have any real values satisfying that part.

Answer 6

So is the whole implication false or true?

Answer 7

F -> anything

is true

Answer 8

if the premisis is False, the implication is true.
so the whole implication is true.

Answer 9

What were you trying to say in the previos comment then?

Answer 10

which comment ?

Answer 11

If x^2 - 2x + 2 ≤ 0, then x^3 ≥ 8. --------------- that part is false, cuz from the hypothesis, x is real, and we dont have any real values satisfying that part.

Answer 12

completing the square on the in-equation in the antecedent, yields an in-equation that is necessarily false.
An implication is true when either,
•its antecedent and its consequent are both true,
or •if the antecedent is false

Answer 13

@UnkleRhaukus I don't see how completing the square results in an inequation that's necessarily false.

Answer 14

Well actually, yes I do, I don't know why I'm saying that.

Answer 15

If a statement is false, that it can imply any other statement. So
x^2 - 2x + 2 ≤ 0, then x^3 ≥ 8 is true
since
x^2 - 2x + 2>0 so x^2 - 2x + 2 ≤ 0 is false.

Answer 16

Obviously an upwards shaped parabola that's raised 2 points off the x-axis isn't going to hit zero ever, so the antecedent is completely, totally, incredibly false.

Answer 17

\[x^2 - 2x + 2 \le 0\\
(x-1)^2+1\le0\\
(x-1)^2\le-1\]
any real number squared is positive

a positive number is never less than or equal to negative one