Let F(x, y) be the predicate that indicates if x and y are friends, with the domain of people. Which of the following statements in predicate logic expresses the statement that

"Every pair of friends has a friend in common"?

(only one correct answer)

a.∀x ∀y [ F(x, y) → ∀z ( (y ≠ z) ∧(x ≠ z) ∧ (F(x, z) ⋁ F(y, z)) ) ]
b.∀x ∀y [ F(x, y) → ∃z ( (y ≠ z) ∧ (x ≠ z) ∧ F(x, z) ∧ F(y, z) ) ]
c.∀x ∀y [ F(x, y) → ∃z ( (y ≠ z) ∧(x ≠ z) ∧ (F(x, z) ⋁ F(y, z)) ) ]