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
-Charles has at least two sons, and so does Elizabeth.
A) (∃x) (∃y) (Sxc • Syc • Sxe • Sye • x≠y)
B) (∀x) (∀y) [(Sxc • Syc) ⊃ x≠y] • (∀x) (∀y) [(Sxe • Sye) ⊃ x≠y]
C) (∃x) (∃y) (Sxc • Syc • x≠y) • (∃x) (∃y) (Sxe • Sye • x≠y)
D) (∀x) (∀y) (∀z) {[(Sxc • Syc) (Sxe • Sye) ] ⊃ (x=z y=z) }
E) (∃x) {Sxc • Sxe • [(∀y) (Syc Sye) ⊃ x=y) ]}
Correct Answer:
Verified
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