Sets, Symbolic Logic

[zealous skiff]

There was a population of peoplepolled on whether they watched either Avatar or Blind
The data given is that the population total is 27
The people who watched both are 3
And that the difference between those who watched only Avatar and those who watched only Blind is of 11 people

Then it asks how many watched Avatar, how many watched Blind, and how many watched neither.

Most I could do is these ecuations to sort the data.

X+Y+Z+3 = 27

Y-X = 11

With X being those who watched only avatar
Y those who only watched blind
And Z those who watched neither.

[paper shale]

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[static notch]

I need to see the original text.

[zealous skiff]

Right, give me a moment to translate it.

[static notch]

A translation isn't the original text.

[zealous skiff]

I meant translate it into english, unless you know spanish, do you still want it that way?

[static notch]

I want to see the original text. If I have questions about it, I will ask them.

[zealous skiff]

Alright then, one second.

[zealous skiff]

Here it is.

[static notch]

See, the first thing I see that might be a mistake is it seems to me like it might be saying |Y - X| = 11.

[zealous skiff]

You don't believe that Y - X = 11? maybe, the line says "Discover that between those who only watched Blind and those who only watched Avatar there are 11 polled (people) of difference."

[static notch]

...that sounds like it's saying x + y = 11.

[zealous skiff]

Missed a bit at the end

the "de diferencia" line was missing.

Sorry

[static notch]

Okay, but unless this is, like, a standardized mathematical language in Spanish, it's not clear to me that it's exactly saying that 11 more people saw only Blind than only Avatar, just that "their difference is 11", which could mean the difference is in either direction.

[zealous skiff]

Difference (diferencia) can be used to mean subtraction in spanish, yes.

[static notch]

...that part I already got.

[zealous skiff]

Alright, so if it just means in either direction.

[static notch]

Look.

Maybe explaining the difference in English will help.

If I say "the difference between 17 and 5 is 12", that's true, because 17 - 5 = 12.

If I say "5 and 17 have a difference of 12", that's also true, but it's a different statement, because I'm not saying that 5 - 17 = 12, I'm saying |5 - 17| = 12.

[zealous skiff]

Right yes, it is possible

so

if you were right and it meant difference in that way.

Where you go from there?

[static notch]

To begin with, x + y + z + 3 = 27, right?

[zealous skiff]

Yeah.

[static notch]

Therefore x + y + z = what?

[zealous skiff]

24

[static notch]

Right.

[zealous skiff]

X and Y are those who only watched the respective movie, and Z are the ones that watched neither, while 3 is the number that watched both.

[static notch]

Also, this is a garbage poll, because what kind of sample size is 27?

[zealous skiff]

A very odd one indeed.

[static notch]

So then, if |x - y| = 11, that of course devolves into two separate cases, right?

Because what's the definition of absolute value?

[zealous skiff]

positive or negative?

So, the distance of the number to 0

[static notch]

The precise definition is as a piecewise function: |x| = x if x >= 0, |x| = -x if x < 0.

[zealous skiff]

I see, I'm thankful for the help you've given me so far, but I'm going to have to go for now as it is very late where I am, if you still want to help it could continue tomorrow.

But, either way, thanks for what was done so far.

[static notch]

No problem, and no worries. It's late here too.

[zealous skiff]

Have a good night

[zealous skiff]

Whenever you have the time, could you tell me if you think there is enough information to go off of to actually finish this problem? I feel like there might not be enough given how it doesn't really tell you any of the actual variables, maybe if one assumed the amount of people that watched neither was 0?

nevermind.