1. (∃x)(Kx $ \lor $ Lx)
2. (∀x)(Jx ⊃ ~Lx)
-Which of the following propositions is derivable from the given premises in M?
A) (∀x)(Kx $ \lor $ Lx)
B) (∀x)(~Jx $ \lor $ Kx)
C) (∃x)(~Jx $ \lor $ Kx)
D) (∃x)~Jx
E) (∃x)Kx

Question

Quizplus · Accepted Answer

Using the first premise, we know that there exists an x such that Kx or Lx is true. However, we cannot conclude anything about Kx or Lx for all x. Using the second premise, for all x, if Jx is true, then ~Lx is true. Combining this with the first premise, we can conclude that there exists an x such that Jx is false and ~Lx is true, which means ~Jx or Kx is true. Therefore, proposition C is derivable.

1 (∃X)(Kx ∨ \lor ∨ Lx) 2 (∀X)(Jx ⊃ ~Lx) -Which of the Following Propositions Is

1 (∃X)(Kx $\lor$ Lx)
2 (∀X)(Jx ⊃ ~Lx)
-Which of the Following Propositions Is