select the best translation into predicate logic, using the following translation key:
a: Ahmed
b: Bhavin
c: Chloe
d: Delfina
e: Eduardo
i: Irving
f(x): the father of x
g(x): the mother of x
f(x,y): the only son of x and y
Lxy: x loves y
Sxy: x is a sister of y
Txy: x teaches y
-No one is the only son of Ahmed and Delfina.
A) (∀x)(x≠a • x≠d)
B) (∀x)f(x,x)≠f(a,d)
C) ∼(∃x)x=f(a,d)
D) ∼(∃x)f(x)
E) ∼(∃x)f(x)=f(a,d)

Question

select the best translation into predicate logic, using the following translation key: 
a: Ahmed
b: Bhavin 
c: Chloe 
d: Delfina
e: Eduardo 
i: Irving
f(x): the father of x
g(x): the mother of x
f(x,y): the only son of x and y 
Lxy: x loves y
Sxy: x is a sister of y 
Txy: x teaches y
-No one is the only son of Ahmed and Delfina.
A) (∀x)(x≠a • x≠d)
B) (∀x)f(x,x)≠f(a,d)
C) ∼(∃x)x=f(a,d)
D) ∼(∃x)f(x)
E) ∼(∃x)f(x)=f(a,d)

Quizplus · Accepted Answer

C is the best choice because it translates the statement directly into predicate logic using negation, whereas the other choices use more complex expressions.

Select the Best Translation into Predicate Logic, Using the Following