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

question 139

Multiple Choice

(∀x) [Px ⊃ (∃y) Rxy] ⊃ [(∀x) (∀y) ∼Rxy ⊃ ∼(∃x) Px]
-Consider assuming '(∀x) [Px ⊃ (∃y) Rxy]' for a conditional proof of the above logical truth. Which of the
Following propositions is a legitimate second step in that proof?

• A) Assume '~(∃x)Px' for a nested conditional proof.
• B) Assume '(∀x)(∀y)∼Rxy' for a nested conditional proof.
• C) Assume '~(∀x)(∀y)~Rxy' for a nested indirect proof.
• D) Px ⊃ (∃y)Ryy
• E) Py ⊃ (∃y)Ryy

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