Thank you so much!

And please help me with those as well:

===========Problem 1===============
Domain: All the people in the world.
L(x,y) : "x loves y"

1) Nobody loves everybody
2) there is somebody whom no one loves.
3) there is exactly one person whom everybody loves.
4) there are exactly two people whom Lynn loves.
5) there is someone who loves no one besides himself or herself
============Problem 2===============
F(x,y): "x can fool y"

1) no one can fool both Fred and Jerry.
2) there is exactly one person whom everybody can fool
3) there is someone who can fool exactly one person besides himself or herself.
NS: not allowed to use $\displaystyle \exists$ !

Please help me explain how to use quantifier to express those statements.I had read through the textbook and everything, but does not make a lot of sense to me.

I do appreciate if you could help me out.