1. (∃x)(∃y)(Dx • Exb • Dy • Eyb • x≠y)
2. (∀x)(Dx ⊃ Ebx)
-Which of the following propositions is derivable from the given premises in F?
A) ~(∃x)(Dx • Exx)
B) (∃x)(∃y)(Ebx • Exb • Eby • Eyb • x≠y)
C) (∀x)(Ebx ⊃ Dx)
D) ~(∃x)(∃y)(Dx • Dy • Exy)
E) (∀x)(∀y)[x≠y ⊃ (Dx $ \lor $ Dy)]

Question

Quizplus · Accepted Answer

The first premise states that there exist at least two distinct entities x and y such that both are D and both are E to b, and they are not the same. The second premise states that for all x, if x is D then x is E to b. From these, we can derive that there exist at least two distinct entities x and y such that both are E to b and both are E from b, satisfying the conditions in choice B. This follows because the first premise guarantees the existence of such entities and their relationship to b, and the second premise's universal condition applies to any entity that is D, ensuring they are also E to b.

1 (∃X)(∃y)(Dx • Exb • Dy • Eyb • X≠y) ∨ \lor ∨

1 (∃X)(∃y)(Dx • Exb • Dy • Eyb • X≠y) $\lor$