Quantifiers

• Disprove the Claim That All Birds Can Fly
  Disprove “all birds can fly” with a counterexample: penguins are birds but cannot fly through the air. See the matching logic in predicate form.
• What Is a Counterexample to ∀x∃y (x = 1/y)?
  Over the real numbers, x = 0 is a counterexample: no nonzero real y has reciprocal zero. The answer depends on the domains.
• How to Prove (∀x P(x) → A) → ∃x(P(x) → A)
  A classical proof uses cases on A and requires a nonempty domain; the statement is not generally valid in intuitionistic logic.