I'm very confused as to how to interpret predicate logic statements with multiple universal quantifiers sharing the same domain. For example, I'm trying to make sense of the following statement:
CM is the domain of all Cabinet Ministers
MS is the domain of all movie stars
L(x,y): person x likes person y
∀c1 ∈ CM, ∀c2 ∈ CM,c1≠c2 -> ∃s ∈ MS, L(s,c1) ^ L(s, c2) ^ (∀c3∈CM, c1≠c3^c2≠c3 -> ~L(s,c3))
I have no idea what this could mean. It seems to me that it's saying all cabinet ministers are either liked or disliked by a movies star. I interpret ∀c1 ∈ CM to be all cabinet ministers but how can there be ∀c1 ∈ CM and ∀c2 ∈ CM? Are all cabinet ministers split in two groups?