Let L$($x$,$ y$)$ be the open sentence $$x loves y$,$ where the universal set consists of all people. Use quantifiers and logical connectives to express each of the following English statements.

$($a$)$ Everybody loves somebody.

$($b$)$ Nobody loves everybody.

$($c$)$ There is somebody whom no one loves.

$($d$)$ There is exactly one person whom everybody loves.