Convert the following logical sentences to CNF$,$ showing each step $($include the name of each logical equivalence as you use it$).$

a$)(($A $$ B$)$ C$)($A $$ C$)(($C $$ D$)$E$)$

b$)(($A $$B$)($C $$ D$))($D $$ A$)$

c$)$ A $$ B $$ C $$ B $$ C $$ D

d$)($A $$B$)(($C $$ D$)($D $$ F$))$

Translate the following natural language statements into first$-$order logic $($FOL$)$ expressions.

"Every student loves logic."

"A person's mother's brother is that person's uncle."

"Every child has a mother."

"All birds can fly, except for penguins."

"Someone in the room is a spy$."$

"Every person who loves someone hates anyone who loves everyone."

$"$No one can win the race without training."

"There is a tallest mountain."

Ex: "All dogs are friendly.": $$x $($Dog$($x$)->$ Friendly$($x$))$