How good are you guys at quantifiers in discrete math...

How good are you guys at quantifiers in discrete math? I've looked online for a similar question and can't seem to find one, wanna help me out?

Fuck, I forgot to add the actual question. I have to prove that or provide a counter example.

I have a counter example, in a way. It works if one of the two are both integers and not fractions., though I'm not sure how to go about using the Y variable because it doesn't have a "for all" or "for every" notation symbol next to it.

So what's the counterexample?

Also go to /sci

Well, if y and x both equal a fraction the argument is incorrect. The problem I have with that is I'm not sure if I'm allowed to change y at all because it has no quantifier.

Yeah I'm a math major. What's the frac() function. I'll answer what you need

frac(x) = x - floor(x)

frac(1/3) + frac(1/3) is not equal to frac(2/3)?

Thanks, also that first quantified statement isn't true by that definiton. To show a universal quantifier false you need to find a single counter example. In this case x=.5, y=.5 is one.

Yeah I thought that, but I wasn't sure if you could change the y variable to whatever you want because it, in itself, did not have a quantifier.

But that makes sense too, thanks user.

you're allowed to change y. if the statement were true, then it holds in any context (i.e., for any y). hence you only need to provide a single counterexample (in any context)

Also keep this thread alive. I'll write out an explanation real quick

Alright user, there's another part to the question anyway, should be able to do that one now.

That one would be correct, I guess the sum would have to go over the ceiling of the lowest number out of the two?

Does that explanation make sense?
Also anything else? I'm super bored

Yeah I have another, this is the following question. I took a picture, but apparently the file is too large:
ForAllx, ForAlly, floor(x+y) >= floor(x) + floor(y)

...

Do you need to prove or disprove that? Or figure out if it's true or not and then prove or disprove it?

Same as before, either prove it's correct or just provide a counter example. It's correct, I'm just a bit lost on how to prove it.

Give me two seconds

There you go, Sup Forumsrother.

Perfect thanks, this helps a lot.

That capital R stands for the set of real numbers and that funny 'e' next to it means 'a member of'. I realized you might not know that notation

This is actually Discrete Mathematics 2, but it's a second year course so I've just forgotten everything. Last year I could've done this in my sleep, but now, dealing with this and Algorithms Design and Analysis I just haven't had time to catch up :/. But now since I've got help, I can go through everything before my test next week.

I don't know anything about comp sci. But literally all I do is prove for all my classes.