Answer:
a) ∀x∃y ¬∀zT(x, y, z)
∀x∃y ∃z ¬T(x, y, z)
b) ∀x¬[∃y (P(x, y) ∨ Q(x, y))]
∀x∀y ¬ [P(x, y) ∨ Q(x, y)]
∀x∀y [¬P(x, y) ^ ¬Q(x, y)]
c) ∀x ¬∃y (P(x, y) ^ ∃zR(x, y, z))
∀x ∀y ¬(P(x, y) ^ ∃zR(x, y, z))
∀x ∀y (¬P(x, y) v ¬∃zR(x, y, z))
∀x ∀y (¬P(x, y) v ∀z¬R(x, y, z))
d) ∀x¬∃y (P(x, y) → Q(x, y))
∀x∀y ¬(P(x, y) → Q(x, y))
∀x∀y (¬P(x, y) ^ Q(x, y))
