The equivalence of \(¬ ∃ x \ Q (x)\) is :

Answer: ¬∃x Q(x) is equivalent to ∀x ¬Q(x).

Reasoning:

1. If ¬∃x Q(x) holds, then there is no x for which Q(x) is true. Therefore, for every x, Q(x) is false, i.e. ∀x ¬Q(x).

2. Conversely, if ∀x ¬Q(x) holds, then there is no x that satisfies Q(x), so ¬∃x Q(x) holds.

This is the quantifier version of De Morgan's laws: ¬∃x P(x) ≡ ∀x ¬P(x) (and similarly ¬∀x P(x) ≡ ∃x ¬P(x)).