1. (∃x){Ex • Fx • (∀y)[(Ey • y≠x) ⊃ Gxy]}
2. En • ∼Fn
-Which of the following propositions is derivable from the given premises in F?
A) (∃x)(Ex • Gxn)
B) Gnn ⊃ ~(∃x)(x≠n • Gxn)
C) (∀x)(Ex ⊃ Gnx)
D) Gnn ⊃ ~(∀x)(x≠n ⊃ Gxn)
E) (∀x)[(Ex • Fx) ⊃ (Gxn $ \lor $ Gnx)]

Question

Quizplus · Accepted Answer

The first premise states that there exists an x such that Ex, Fx, and for all y, if Ey and y is not x, then Gxy. The second premise states that En and not Fn. From these, we can derive that there exists an x such that Ex and Gxn, which corresponds to choice A.

1 (∃X){Ex • Fx • (∀Y)[(Ey • Y≠x) ⊃ Gxy]} ∨ \lor ∨

1 (∃X){Ex • Fx • (∀Y)[(Ey • Y≠x) ⊃ Gxy]} $\lor$