# What does this formal sentence mean for the given interpretation?

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".

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)

• 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. – Nick R May 13 '18 at 17:34
• Thank you! I was really concerned that I couldn't answer such a basic question – Liam Donovan May 13 '18 at 17:37
• You are correct. The provided answer is not. – Bram28 May 13 '18 at 17:43