screenshot of question If the domain is the natural numbers and R(x,y) is interpreted as ("x is the square of y"), I would interpret ∀X∃yR(y,x) as meaning "the square of any natural number is a natural number".

screenshot of question

However, the correct interpretation of sentence b is apparently "every natural number has a square root that is a natural number". Why is this? To ensure I haven't just misread something, I've included screenshots of the question and answer (this is from a practice exam for a philosophy course)

screenshot of answer

  • 1
    I agree with you. As stated, (b) says that the square of any natural number is a natural number. One possible explanation for the "correct" interpretation is that there is a typo. Note that the relation is written as "Ry,x" in (b), rather than "Rx,y". If they meant to say "Rx,y" then their "correct" answer would hold.
    – nwr
    May 13, 2018 at 17:34
  • Thank you! I was really concerned that I couldn't answer such a basic question May 13, 2018 at 17:37
  • You are correct. The provided answer is not.
    – Bram28
    May 13, 2018 at 17:43


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