- #1
NasuSama
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Homework Statement
A universal (or ∀_1) formula is one of the form ∀x_1∀x_2...∀x_nθ, where θ is quantifi er-free.
An existential (or ∃_1) formula is one of the form ∃_1∃_2...∃x_n θ.
Let A be a substructure of B, and s valuation on A.
a) Show that if ⊨_B ψ
b) Use part (a) to show that the sentence (∃x Px) is not logically equivalent to any universal formula, and that (∀x Px) is not logically equivalent to any existential formula.
Homework Equations
→satisfiability?
The Attempt at a Solution
My professor goes too quickly with satisfiability, and he expects me to solve such problem.
Here are some thoughts I have..
a) Since ψ is universal, we can say that ⊨_B ∀x_1∀x_2...∀x_n θ
Seems like I lack some understanding of how the proof should work. -___-
b) I am not sure how to work out part b.