∀x . ∃y . C(x)→(H(y)∧L(x,y))
You can pick anyone you want (call them x);
	then I'll pick someone (call them y) such that
		if x is in the class
		then y is happy and x likes y.

∃y  .  ∀x  .  C(x)→(H(y)∧L(x,y))
I can pick someone (call them y) such that
	no matter who you pick (call them x)
		if x is in the class
		then y is happy and x likes y.


Everyone (in and out of the class) likes at least one happy person.

∀∃ order:
	I can do it. (⊤)
	You pick someone, I pick the happy person they like.
∃∀ order:
	I can't do it. (⊥)
	I pick someone, you can pick someone in the class that doesn't like them.


The class is empty; no one is in it.
∀∃ order:
	I can do it. (⊤)
	The if-then never applies, so this is vacuuously true.
∃∀ order:
	I can do it. (⊤)
	The if-then never applies, so this is vacuuously true.


There's only one happy person in the world.
∀∃ order:
	I can do it iff everyone in the class likes that person. 
		(∀x . C(x) → L(x, the happy person))
∃∀ order:
	I can do it iff everyone in the class likes that person. 
		(∀x . C(x) → L(x, the happy person))