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Homework Help: Transforming predicate form to quantifiers

  1. Feb 3, 2015 #1
    1. The problem statement, all variables and given/known data
    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+

    2. Relevant equations
    The fact that ∀ is universal and ∃ is existential.

    3. 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?
  2. jcsd
  3. Feb 4, 2015 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    "Has a solution" means "there exists a solution".
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