I am currently confused, below I have a statement and my expression of that statement in first order logic.
R(person, song, album)
Statement: Every song that Gershwin wrote has been recorded on some album.
Answer: ∀y W(G, y) ⇒ ∃a R(G, y, a)
However, my textbook answer
Answer: ∀y W(G, y) ⇒ ∃a,p R(p, y, a)
Instead of using Gershwin in the argument of R, why did it instead say there exists a person p? Does it really make a difference or am I still unclear about how expressing statements in first order logic work?