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Database miscellaneous

  1. Which one of the following is not logically equivalent to ̚ ∃x (∀ y (α) ∧ ∀ z (β) ) ?
    1. ∀ x (∃z ( ̚ β ) → ∀ y (α) )
    2. ∀ x (∀z ( β ) → ∃ y (̚ α) )
    3. ∀ x (∃y ( α) → ∃ z (̚ β) )
    4. ∀ x (∃y ( ̚ α ) → ∃ z (̚ β) )
Correct Option: A

∀ ×(∃z(̚β) &rarrr; ∀ y(α)) and ∀ ×(∃y(̚α) &rarrr; ∃z(β)) both are NOT logically equivalent to
̚∃ × (∀y(α) ∧ ∀z(β)



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