I couldn't be sure about the negation of the statement $\exists x \in N , x < 3$
is it $$ \lnot(\exists x \in N , x < 3) \equiv (\forall x \in N , x \geq 3) $$ or $$ \lnot (\exists x \in N , x < 3) \equiv (\forall x \notin N , x \geq 3) $$ can someone help me (with an explanation)?