Show that the following two propositions are logically equiv

Show that the following two propositions are logically equivalent; and

Solution

Two statements S and T involving predicates and quantifiers are logically equivalent if and only if they have the same truth value regardless of the interpretation, i.e. regardless of the meaning that is attributed to each propositional function, the domain of discourse

We denote S ? T.

and in this case

when we remove the negation sign from the 1st predicate statement

then precidence and quantifier are exachanged

and so from there we can say that 2 statement are equivalent