# 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.
– 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. May 13, 2018 at 17:43