Assume $X = \{a,b,c,d,e\}$
where $a$ is friends with everyone in class $X$ except $e$ and $d$ and $e$ and $d$ are friends with each other.
let J(x,y) be x and y are friends
1. $(∀x)(∃y) J(x,y) \equiv (∃y)(∀x) J(x,y)$
$(∀x)(∃y) J(x,y) $ means for all x there is a y for which J(x,y) is true
also it will be false if there is someone in class $X$ which will not be having any friend.
it also means "Everyone in class X will have some friend"
So this is true considering set $X$
now lets check $(∃y)(∀x) J(x,y)$
this means 'there is someone in class who is friends with everyone'
now this is false because no one exists who is friends with everyone
hence $(∀x)(∃y) J(x,y) \not\equiv (∃y)(∀x) J(x,y)$
2nd question asked by you is no different
3rd and 4th are true and meaning of statement does not change if we switch the position of quantifiers if both quantifiers are same.
