The biconditional relationship [(?x)Nx] ? [~(x)~Nx] tells us that the universal and
existential quantifiers negate each other, and so the two quantifiers may never be
transformed into one another.

Question

The biconditional relationship [(?x)Nx] ? [~(x)~Nx] tells us that the universal and
 existential quantifiers negate each other, and so the two quantifiers may never be
 transformed into one another.

Quizplus · Accepted Answer

The biconditional relationship [(∀x)Nx] ↔ [~(∃x)~Nx] shows the logical equivalence between a universal statement and the negation of an existential statement with its predicate negated. This means that the universal quantifier can be transformed into a negated existential quantifier with a negated predicate, and vice versa, indicating they can be related or transformed into one another under negation.

The Biconditional Relationship [(?X)Nx] ? [~(X)~Nx] Tells Us That the Universal