Select the Best Translation into Predicate Logic, Using the Following $\lor$

question 202

Multiple Choice

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
-Any son of Elizabeth or Charles is more exalted than anyone who is not Charles, Elizabeth, or a son of either.

• A) (∀x)[(Px • x≠e • x≠c • Sxe • Sxc) ⊃ (∀y)(Py ⊃ Exy)]
• B) (∀x){(Sxe \( \lor \) Sxc) ⊃ (∀y)[(Py • y≠c • y≠e • ~Sye • ~Syc) ⊃ Exy]}
• C) (∀x)(∃y){(Eyx • Py) ⊃ [(Sxe \( \lor \) Sxc) ⊃ (y=e \( \lor \) y=c \( \lor \) y=x)]}
• D) (∀x){(∃y)(Eyx • Py) ⊃ [(Sxe \( \lor \) Sxc) ⊃ (Ecx • Eex)]}
• E) (∀x){[(Sxe \( \lor \) Sxc) • x≠c • x≠e] ⊃ (∀y)(Py ⊃ Exy)}

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