1. ## symbolic to verbal

I need to write this in verbal form:

$\displaystyle (\forall x \in Z) (x > 0 \vee (\exists y \in Z) (y ^{2} = x))$

I think I'm usually pretty good at this, but all those parentheses are really throwing me off

This is what I have so far:

Given any integer x, if x is greater than zero or there is an integer y such that y squared equals x

Am I on the right track?? Is tehre a simpler form?

2. Originally Posted by relyt
I need to write this in verbal form:

$\displaystyle (\forall x \in Z) (x > 0 \vee (\exists y \in Z) (y ^{2} = x))$

I think I'm usually pretty good at this, but all those parentheses are really throwing me off

This is what I have so far:

Given any integer x, if x is greater than zero or there is an integer y such that y squared equals x

Am I on the right track?? Is tehre a simpler form?
no. saying "if" means you are describing an implication, which is not the case here. you have an expression of the form $\displaystyle (\forall x \in A)[P(x) \vee (\exists y \in A)Q(x,y)]$

it is translated as: "for every $\displaystyle x \in A$, either $\displaystyle P(x)$ or there exists $\displaystyle y \in A$ such that $\displaystyle Q(x,y)$"

3. That's pretty cool Jhevon! I'm studying this at the moment, so what you are saying is that there are two propositions of the form P $\displaystyle \vee$ Q. And the quantifiers remain unchanged?
I'm not used to using brackets used like this, either. Are these two statements the same:

$\displaystyle \forall x \in \mathbb{Z}x>0) \vee \exists y \in \mathbb{Z}y^2=x)$

Or have I missed something with the either ... or?

4. Originally Posted by relyt
I need to write this in verbal form:
$\displaystyle (\forall x \in Z) (x > 0 \vee (\exists y \in Z) (y ^{2} = x))$
I would translate this way: Every integer is positive or it is the square of some integer.

5. Thanks, guys. I think I got it down now. Much appreciated!

So for the set N of positive integers...this statement: "Every integer is the sum of two other integers".

would be
$\displaystyle (\forall x \in N+)(x = y + z)$

??