1. (∀x)[(Px $ \lor $ Qx)] ⊃ Rxx]
2. (∀x){Qx ⊃ [(∃y)Rxy ⊃ Sxx]}
3. Pn • Qn
-Which of the following propositions is derivable from the given premises in F?
A) Rnn • Snn
B) (∀x)Rnx
C) (∀x)Rxn
D) (∀x)(Px ⊃ Sxx)
E) Rnn ≡ ~Snn

Question

Quizplus · Accepted Answer

From the premises, we can derive Rnn and Snn. The first premise, when applied to 'n' (given Pn • Qn, meaning both Pn and Qn are true), ensures Rnn is true. The second premise, given Qn, allows for the derivation of Snn if there exists some y such that Rny, which is confirmed by Rnn. Thus, Rnn • Snn is derivable.

1 (∀X)[(Px ∨ \lor ∨ Qx)] ⊃ Rxx] 2

1 (∀X)[(Px $\lor$ Qx)] ⊃ Rxx]
2