I am thinking about whether this is valid or not;
∃x∀y (P(x,y)) ↔ ∀x∃y (P(x,y))
My attempt so far; Let's assume that P(x,y) function represents that x and y are friends, on the left side of the statement it says "At least 1 person in the world is friend with everybody on earth. " and on the right "Whole world is friend with at least 1 common person". Do these mean that right should support left and left should support right, I am confused and can't think of any other function suiting the statement right now. I guess in this case, the statement is valid but I am not sure at all..