Q1: Exercise Show that:
Establishing validity and invalidity
a) |= ∀x(Fx→(Fx ∨ Gx))
b) |= ∀x(Fx ∧ Gx) → (∀xFx∧∀xGx)
c) ∀x(Fx → Gx),∀x(Gx → Hx) |=∀x(Fx → Hx)
d) |= ∃x∀yRxy → ∀y∃xRxy
Q2 :Definite descriptions
Exercise Establish the following:
Symbolize the following sentences using predicate logic with identity and function symbols:
a)**|= ∀xLxtyFxy → ∀x∃yLxy
b) Fx∀y Lxy |= ∀x∀y ((∀zLxz∧∀zLyz) → x=y)