Concept guide
Quantifiers and explicit domains: deciding universal and existential statements and their negations on a finite integer domain
On the explicit finite domain U={−2,−1,0,1,2,3}, decide the truth of φ₁: ∀x∈U, x²<10; φ₂: ∀x∈U, x²>x; φ₃: ∃x∈U, x²=2; write the negations of φ₂ and φ₃ correctly; and settle the truth of universal and existential statements when the domain is the empty set.