select the best translation into predicate logic, using the following translation key:
b: Britain
c: Charles
e: Elizabeth
t: Tescos
Px: x is a person
Qx: x is a Queen of England
Wx: x is a woman
Exy: x is more exalted than y
Ixy: x is in y
Pxy: x shops at y
Sxy: x is a son of y
-All people in Britain shop at Tescos, except Elizabeth.
A) Pe • Ieb • ~Pet • (∀x)[(Px • Ixb • x≠e) ⊃ Pxt]
B) Pe • Ieb • ~Pet • (∀x)[(Px • Pxt • Ixb) ⊃ x≠e]
C) Pe • Ieb • ~Pet • (∀x)[(Px • Pxt • x≠e) ⊃ Ixb]
D) Pe • Ieb • ~Pet • (∀x)[(Px • Ixb) ⊃ Pxt]
E) Pe • Ieb • ~Pet • (∀x)[(Px • Pxt) ⊃ Ixb]

Question

select the best translation into predicate logic, using the following translation key:
b: Britain
c: Charles 
e: Elizabeth 
t: Tescos
Px: x is a person
Qx: x is a Queen of England
Wx: x is a woman
Exy: x is more exalted than y 
Ixy: x is in y
Pxy: x shops at y 
Sxy: x is a son of y
-All people in Britain shop at Tescos, except Elizabeth.
A) Pe • Ieb • ~Pet • (∀x)[(Px • Ixb • x≠e) ⊃ Pxt]
B) Pe • Ieb • ~Pet • (∀x)[(Px • Pxt • Ixb) ⊃ x≠e]
C) Pe • Ieb • ~Pet • (∀x)[(Px • Pxt • x≠e) ⊃ Ixb]
D) Pe • Ieb • ~Pet • (∀x)[(Px • Ixb) ⊃ Pxt]
E) Pe • Ieb • ~Pet • (∀x)[(Px • Pxt) ⊃ Ixb]

Quizplus · Accepted Answer

The statement can be broken down into two parts: 
1. All people in Britain shop at Tescos: (∀x)[(Px • Ixb) ⊃ Pxt] 
2. Elizabeth does not shop at Tescos: ~Pet 
So, the best translation into predicate logic would be: Pe • Ieb • ~Pet • (∀x)[(Px • Ixb • x≠e) ⊃ Pxt], which combines both parts and specifies that Elizabeth is the exception to the first statement. Choice A correctly represents this translation.

Select the Best Translation into Predicate Logic, Using the Following