Q: Which of the following statements about existence and uniqueness in logic are correct?
(A) The statement “Every real number has a unique additive inverse” can be written symbolically as ∀x ∈ ℝ ∃! y ∈ ℝ such that x + y = 0;
(B) The uniqueness quantifier “∃! y” means “there exist infinitely many y”;
(C) To prove uniqueness, it is enough to show that at least one object with the required property exists, without comparing different possibilities;
(D) In logic, the statement “There exists exactly one x such that P(x)” implies both that some x satisfies P(x) and that no two distinct x satisfy P(x);
(E) The statement “For all x there exists a y such that P(x, y)” is logically equivalent to “There exists a y such that for all x, P(x, y)”;
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