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 w=y w=z) ]}
C) (∀x) (∀y) (∀z) (∀w) [(Sxe • Sye • Sze • Swe) ⊃ (x=y x=z x=w y=z y=w 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 x=z y=z) • (∀x) [Swe ⊃ (w=x w=y w=z) ]}
Correct Answer:
Verified
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