(∀X)[Px ⊃ (∃Y)Rxy] ⊃ [(∀X)(∀y)∼Rxy ⊃ ∼(∃X)Px]

question 173

Multiple Choice

(∀x) [Px ⊃ (∃y) Rxy] ⊃ [(∀x) (∀y) ∼Rxy ⊃ ∼(∃x) Px]
-Which of the following propositions is also derivable in F?

• A) (∀x)[Px ⊃ (∃y)Rxy] ⊃ [(∃x)~Px ⊃ (∃x)(∃y)Rxy]
• B) (∀x)[(∃y)Rxy ⊃ ~Px] ⊃ [(∃x)Px ⊃ (∃x)(∃y)Rxy]
• C) (∀x)[Px ⊃ (∃y)Rxy] ⊃ [(∃x)Px ⊃ (∃x)(∃y)Rxy]
• D) (∀x)[~(∃y)Rxy ⊃ Px] ⊃ [(∃x)Px ⊃ (∃x)(∃y)Rxy]
• E) (∀x)[Px ⊃ (∃y)Rxy] ⊃ [(∃x)~Px ⊃ (∃x)(∃y)~Rxy]

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Definitions:

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