Right now I'm working on a set of questions and I came across a two-parter that confused me a bit with the way it was asked. The question is simply put as such:
Write the statements below in symbolic logic. a. Everybody loves somebody. b. Somebody loves everybody.
Would the way to rewrite this be a simple as using existential and universal quantifiers? Such that a. would be translated to
"∀x, where x is a person, ∃ person x they love."
And b. would be translated to
"∃x such that x loves ∀x."
Is this a proper way to answer the question? Any help is appreciated.