Rewrite the statement ¬∃x (∀y∃tS(x, y, t) ∧ ∃tR(x, t)) so that negations appear only within predicates.

Question

Rewrite the statement ¬∃x (∀y∃tS(x, y, t) ∧ ∃tR(x, t)) so that negations appear only within predicates.

Answer 1

¬ simply exchanges ∃ and∀, ∧ and ∨

¬∃x (∀y∃tS(x, y, t) ∧ ∃tR(x, t)) = ∀x (∃y∀t¬S(x, y, t) ∨ ∀t¬R(x, t))