Just a small question regarding the logical negation of a statement:
$∀x (∃y (∀z A(x,y,z)))$ where a is $A$ formula dependant on $x,y,z$.
I know that when negating statements quantifiers are reversed and then the statemnent is negated, but I just want to check the order of statements is correct.
Based on above I worked out:
$∃x (∀y (∃z ¬A(x,y,z))$
But it doesn't quite seem right just thinking about the wording of the statement.
Any help would be greatly appreciated!