Can someone check my answers for me?

e)“Only zero is divided by all natural numbers.”

∀x(∃y(y|x) → (y = 0))

f) ”Each Pythagorean triple involves at least one even number.”∀x∀y∀z((x^2 + y^2 = z^2) → ∀n(x = 2n V y = 2n V z = 2n))

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- Mar 4th 2009, 05:53 PMthehollow89More predicate logic
Can someone check my answers for me?

e)*“Only zero is divided by all natural numbers.”*

∀x(∃y(y|x) → (y = 0))

f) ”*Each Pythagorean triple involves at least one even number.”*∀x∀y∀z((x^2 + y^2 = z^2) → ∀n(x = 2n V y = 2n V z = 2n))

- Mar 4th 2009, 06:45 PMPlato
Passive voice is much more difficult to symbolize that active voice.

Suppose the domain is the set of non-negative integers.

‘Some number is divisible by every number’: $\displaystyle \left( {\exists n} \right)\left( {\forall k} \right)\left[ {k|n} \right]$.

‘Every number is divides some number: $\displaystyle \left( {\forall k} \right)\left( {\exists n} \right)\left[ {k|n} \right]$

Now on the domain the first statement is false, no number is divisible by zero.

But on that domain the second statement is true, 1 divides every number.