Multiple generality

FOL symbolizations with nested and mixed quantifiers, where the order of universal and existential quantifiers changes what a sentence says.

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4 exercises

Using this symbolization key:

domain:
all animals
$A(x)$ :
$\underline{\hskip 15.00002pt}_{x}$ is an alligator
$M(x)$ :
$\underline{\hskip 15.00002pt}_{x}$ is a monkey
$R(x)$ :
$\underline{\hskip 15.00002pt}_{x}$ is a reptile
$Z(x)$ :
$\underline{\hskip 15.00002pt}_{x}$ lives at the zoo
$L(x,y)$ :
$\underline{\hskip 15.00002pt}_{x}$ loves $\underline{\hskip 15.00002pt}_{y}$
$a$ :
Amos
$b$ :
Bouncer
$c$ :
Cleo

symbolize each of the following sentences in FOL:

Using the following symbolization key:

domain:
all animals
$D(x)$ :
$\underline{\hskip 15.00002pt}_{x}$ is a dog
$S(x)$ :
$\underline{\hskip 15.00002pt}_{x}$ likes samurai movies
$L(x,y)$ :
$\underline{\hskip 15.00002pt}_{x}$ is larger than $\underline{\hskip 15.00002pt}_{y}$
$r$ :
Rave
$h$ :
Shane
$d$ :
Daisy

symbolize the following sentences in FOL:

Using the following symbolization key:

domain:
people and dishes at a potluck
$R(x)$ :
$\underline{\hskip 15.00002pt}_{x}$ has run out
$T(x)$ :
$\underline{\hskip 15.00002pt}_{x}$ is on the table
$F(x)$ :
$\underline{\hskip 15.00002pt}_{x}$ is food
$P(x)$ :
$\underline{\hskip 15.00002pt}_{x}$ is a person
$L(x,y)$ :
$\underline{\hskip 15.00002pt}_{x}$ likes $\underline{\hskip 15.00002pt}_{y}$
$e$ :
Eli
$f$ :
Francesca
$g$ :
the guacamole

symbolize the following English sentences in FOL:

Using the following symbolization key:

domain:
people
$D(x)$ :
$\underline{\hskip 15.00002pt}_{x}$ dances ballet
$F(x)$ :
$\underline{\hskip 15.00002pt}_{x}$ is female
$M(x)$ :
$\underline{\hskip 15.00002pt}_{x}$ is male
$C(x,y)$ :
$\underline{\hskip 15.00002pt}_{x}$ is a child of $\underline{\hskip 15.00002pt}_{y}$
$S(x,y)$ :
$\underline{\hskip 15.00002pt}_{x}$ is a sibling of $\underline{\hskip 15.00002pt}_{y}$
$e$ :
Elmer
$j$ :
Jane
$p$ :
Patrick

symbolize the following sentences in FOL: