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

question 238

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
-Elizabeth has exactly three sons.

• A) ~(∃x)(∃y)(∃z)(∃w)(Sxe • Sye • Sze • Swe • x≠y • x≠z • x≠w • y≠z • y≠w • z≠w)
• B) (∃x)(∃y)(∃z){Sxe • Sye • Sze • x≠y • x≠z • y≠z • (∀w)[Swe ⊃ (w=x \( \lor \) w=y \( \lor \) w=z)]}
• C) (∀x)(∀y)(∀z)(∀w)[(Sxe • Sye • Sze • Swe) ⊃ (x=y \( \lor \) x=z \( \lor \) x=w \( \lor \) y=z \( \lor \) y=w \( \lor \) w=z)]
• D) (∃x){{Sxe • (∃y){Sye • (∃z)[Sze • (∀w)(Swe ⊃ w=z)]} ⊃ w=y} ⊃ w=x}
• E) (∃x)(∃y)(∃z){Sxe • Sye • Sze • (x=y \( \lor \) x=z \( \lor \) y=z) • (∀x)[Swe ⊃ (w=x \( \lor \) w=y \( \lor \) w=z)]}