I'm having trouble understanding predicate logic. I get very confused in interpreting the parentheses, to be able to correctly demarcate the scope of quantifiers, particularly in the following (from our unit book):
(x)(Bx → (Cx & ~Dx)) & ((∃y)(Ey & Fy) v (∃z)((~Jz & ~Kz) → (w) Mwz))
Is this correct? Can you please explain where I'm wrong? Thank you!
(x) : Scope is (Bx → (Cx & ~Dx). The x in Bx, Cx, and ~Dx, are bound to (x).
(∃y) : Scope is (Ey & Fy). The y in Ey and Fy are bound to (∃y).
(∃z) : Scope is (~Jz & ~Kz) → (w) Mwz). The z in ~Jz, ~Kz, and Mwz, are bound to (∃z).
Yes, all correct. Also, the scope of the $(w)$ is $Mwz$