Translate it
A: actor
L: loves
j: Jim
"Jim doesn't love any actors"
(∀x)(Ax ⊃ ∼Ljx)
or
(∀x)∼(Ax ⋀ Ljx)
or
∼(∃x)(Ax ⋀ Ljx)
A: actor
L: loves
j: Jim
"Jim doesn't love any actors"
(∀x)(Ax ⋀ ∼Ljx)
this translates to:
"Everyone is an actor and Jim doesn't love anyone"
A: actor
L: loves
j: Jim
"Jim doesn't love any actors"
(∀x)(Ax ⊃ ∼Lxj)
This translates to:
"no actors love Jim".
A: actor
l: loves
J: Jim
"Jim doesn't love any actors"
∼(∃x)(Ax ⋀ Jlx)
This translation confuses general and particular terms.
m: Mark
r: Rupert
P: is a person
"Mark and Rupert are different people"
(~(m=r)⋀(Pm ⋀ Pr))
m: Mark
r: Rupert
P: is a person
"Mark and Rupert are different people"
((m=~r)⋀(Pm ⋀ Pr))
This translates to:
"Anyone other than Rupert is Mark, and both Mark and Rupert are people."
m: Mark
r: Rupert
P: is a person
"Mark and Rupert are different people"
((Pm ⋀ Pr)⊃ ~(m=r))
This translates to:
"If Mark is a person and Rupert is a person, then Mark is not Rupert or vise versa"
"Mark and Rupert are different people"
((m≠r)⋀(Pm ⋀ Pr))
That is a nonconventional symbol for identity.
R: is rich
"Exactly one being is rich"
(∃x)(Rx ⋀ ∼(∃y)(~x=y ⋀ Ry)
R: is rich
"Exactly one being is rich"
(∃x)Rx
this translates to:
"At least one being is rich"
"Everyone loves someone"
(∀x)(∃y)Lxy
"Everyone loves someone"
(∃y)(∀x)Lxy
This translates to:
"There is someone that everyone loves"