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## Homework Statement

Write the following statements in predicate form, using logical operators ^,∨, (NOT - negation but don't know where the symbol is :/) , and quantifiers ∀,∃. Below ℤ

^{+}denotes all positive integers {1,2,3,.....}.

I need help with this first statement:

For any x, y ∈ ℤ

^{+}the equation x

^{2}+ y

^{2}- z = 0 has a solution z

∈ ℤ

^{+}

## Homework Equations

The fact that ∀ is universal and ∃ is existential.

## The Attempt at a Solution

I can't seem to figure out where to start... I just got ∀x∀y ( x

^{2}+ y

^{2}= z) which seems wrong to me. any help?