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Transforming predicate form to quantifiers

  • Thread starter MarcL
  • Start date
  • #1
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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 x2 + y2 - 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 ( x2 + y2 = z) which seems wrong to me. any help?
 

Answers and Replies

  • #2
Stephen Tashi
Science Advisor
7,020
1,244
"Has a solution" means "there exists a solution".
 

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