# symbolic to verbal

• March 28th 2009, 08:05 PM
relyt
symbolic to verbal
I need to write this in verbal form:

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

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?
• March 28th 2009, 10:10 PM
Jhevon
Quote:

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

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

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 $(\forall x \in A)[P(x) \vee (\exists y \in A)Q(x,y)]$

it is translated as: "for every $x \in A$, either $P(x)$ or there exists $y \in A$ such that $Q(x,y)$"
• March 29th 2009, 12:22 AM
bmp05
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 $\vee$ Q. And the quantifiers remain unchanged?
I'm not used to using brackets used like this, either. Are these two statements the same:

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

Or have I missed something with the either ... or?
• March 29th 2009, 04:15 AM
Plato
Quote:

Originally Posted by relyt
I need to write this in verbal form:
$(\forall x \in Z) (x > 0 \vee (\exists y \in Z) (y ^{2} = x))$

I would translate this way: Every integer is positive or it is the square of some integer.
• March 29th 2009, 07:37 AM
relyt
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
$(\forall x \in N+)(x = y + z)$

??