1. (∀x)(Ax ⊃ Bx)
2. (∃x)Ax
3. (∃x)Bx ⊃ (∃x)Dx
-Which of the following propositions is derivable from the given premises in M?
A) (∃x)Dx
B) (∀x)Bx
C) (∃x)(Dx • Bx)
D) (∀x)(Dx • Bx)
E) (∀x)Ax

Question

Quizplus · Accepted Answer

From premise 2, we know that there exists an x such that Ax is true. From premise 1, this implies that Bx is also true for that same x. Then, from premise 3, we have that if there exists an x such that Bx is true, then there exists an x such that Dx is true. So, we can conclude that there exists an x such that Dx is true (by modus ponens), which is represented by the proposition (∃x)Dx.

1. (∀X)(Ax ⊃ Bx)