"Prove these logical equivalences, assuming that the domain is nonempty."
"You will probably have to use a proof by cases on the two possible values of proposition"
"∀yQ(y) and ∃yQ(y) respectively. This proof will use word arguments (not symbolic formula manipulation)."
"(a) ∀x(∀yQ(y) → P (x)) ≡ ∀yQ(y) → ∀xP (x)"

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