1. (∀x)(∀y)(∀z)[(Ix • Jx • Iy • Jy • Iz • Jz) ⊃ (x=y $ \lor $ y=z $ \lor $ x=z)]
2. Ia • Ja • Ka • Ib • Jb • Kb • a≠b
-Which of the following propositions is derivable from the given premises in F?
A) (∀x)[(Ix • Jx) ≡ (a=x • b=x)]
B) (∀x)[Kx ⊃ (Ix • Jx)]
C) (∀x)[(x≠a • x≠b) ⊃ ~(Jx $ \lor $ Ix)]
D) (∀x)[(Ix • Lx) ⊃ (x=a $ \lor $ x=b $ \lor $ ∼Jx)]
E) (∀x)[(Kx • Lx) ⊃ Jx]

Question

Quizplus · Accepted Answer

From premise 1, we can derive that if any two of x, y, and z have the same property of being I or J, then they must be equal. Using this, we can derive that a and b cannot have the same property of being I or J since a ≠ b, and therefore, Jx must be false for any x that is neither equal to a nor equal to b. This allows us to derive proposition D, which states that for any x that is I, if Lx is also true, then either x=a, x=b, or Jx is false.

1 (∀X)(∀y)(∀z)[(Ix • Jx • Iy • Jy • Iz ∨ \lor ∨

1 (∀X)(∀y)(∀z)[(Ix • Jx • Iy • Jy • Iz $\lor$