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)