Question

In the domain of all integers, use the predicates below to write the statement as a formula using the appropriate quantifies.

"Every prime number greater than 3 is the sum of two prime numbers."

* P(x) = " is a prime number."
* G(x, y) = "x > y"
* S(x, y, z) = "x = y + z"

Answer 1

Hmm :d

Answer 2

I'm thinking they want something along these lines... maybe...

For all \(\rm x\in\mathbb Z\), if \(\rm x\in P\) and ...
no no no.. they're doing something else fancy here.
Hmm, trying to make sense of this.

Do you have an example problem maybe?

Answer 3

I don't, sorry

Answer 4

Ok maybe it's as simple as this...

Answer 5

`For every x in P(x),`
`If G(x,3)` <-- This is saying if x is greater than 3,
read your definition of G(x,y) again if that's confusing.
`Then S(x, y, z) where y, z are also in P`.

Answer 6

Grr I dunno, something like that... hmm

Answer 7

That looks to me like it would be correct also, or at least close to it. Does that specify that x is the sum of "prime" numbers?

Answer 8

I find it a little confusing that they're using this y value in both G and S.
In G it's clear that it should be 3 for the y value.
We want our prime number to be greater than 3.

But we don't want to use this value for the sum in S.
x could be the sum of two different primes,
not necessarily 3 being one of them.

But yes, the y and z should also belong to this group P.
For all x in P(x)
If G(x,3),
Then S(x,y,z), where y, z are in P(x).

We're calling it P(x) though, hmm...

Answer 9

Bahh math is hard >.<

Answer 10

Or maybe this is better,
For all x in P(x), there exists y,z in P(x) such that,
if G(x,3)
then S(x,y,z)

Stating where y and z are at the start seems to make more sense.

Answer 11

Yes it is ha. Ohhh, I see now. Do you think this would make sense?:

For every x such that P(x)((G(x, y)) there exists some x and some y such that P(x) such thatS(x, y, z)

??

Answer 12

It's a little hard to understand because I can't type in the right symbols

Answer 13

Maybe like this:
For every x such that P(x) and G(x,3),
there exist some y and z such that S(x,y,z)

You certainly don't want to say something about "every x"
and then connect that to "there exists an x"
that doesn't really make sense :)

Answer 14

*There exists some y and z such that P(y) and P(z) and S(x,y,z)

Answer 15

For the last line, I didn't say anything about y and z being prime.
Maybe that corrects it.

Answer 16

Ok, I think the way you said it is actually the way I have it down on paper. Do you think pecifying that they are prime could maybe be something like:

there is some why and some z such that P(y)^P(z)

?

Answer 17

\[\large\rm \exists y,z:P(y)\wedge P(z)\wedge S(x,y,z)\]Using your "and" modifier?
Yah that seems good.
I think you want to chain it together with your Sum statement like this though.
Unless you had something else in mind.

Answer 18

Math Logic is some goofy stuff, huh? :) lol

Answer 19

Hat is exactly what I have written, thanks. It is very goofy lol