First$-$Order Logic$/$ Predicate Logic

$1-$ Explain how first$-$order logic differs from propositional logic.

$2-$ Give an example of the key parts of first$-$order logic.

$3-$ How do the universal, existential quantifiers and negation relate?

$4-$ What is the meaning of the following FOL formulas natural language?

a$.$ bought$($Frank$,$ dvd$)$

b$.$x$.$bought$($Frank$,$ x$)$

c$.$ bought Frank, $x$ bought Susan, $x$

d$..$ bought Frank, $x$ Susan, $x$

e$.$ AAxEEy$*$ bought $(x,y)$

f$.,$EExAAy.bought$(x,y)$

g$.,$EEsAAh Student$($s$){?}^{{?}^{?}}$ Taking$($s$,$AI$){?}^{{?}^{?}}$ HomeworkFor$($h$,$AI$){?}^{{?}^{?}}$notHates$(s,h)$

h$.,$AAx Mushroom $(x)=>$not$(Poisonous(x{)}^{{?}^{?}}$Purple$(x))$

$5-$ Convert the following into FOL statements.

All cats are cute.

All students taking AI are genius.

Some students taking AI are genius and hardworking.

There is a bunny who is a cute. $($some bunnies are cute$)$

$6-$ Answer the following question: