Post Office Burglary

Remember that one statement of each person has to be true and one statement has to be false. Look at the statement of Eden : " It was Dabney. It was Aage." If one statement is true, one statement is false then either Dabney or Aage committed the crime. Now look at Babson's statement :" It wasn't Cade. It was Aage. " We know that Cade hasn't done it. So this statement is true. This means the statement " It was Aage ." is false making Dabney the culprit.

The first two witnesses gave opposite statements, so both their accusations must be false (since we know that they gave one false statement each and the options hint at a sole criminal), so Cade and Aage are innocents.

Looking at Eden's statements, her second one on that accusation against Aage must be false since Aage's innocence was already established before, so her first accusation against Dabney must be the truth.

Dabney is guilty of PO burglary.

Going with Eden's saying, either Dabney or Aage had to do it. Dabney said Cade did it, and Aage didn't. Cade couldn't have done it, so Dabney didn't lie about Aage, leaving Eden saying Dabney did it as the truth.

Eden's statements are: "It was Dabney, It was Aage". One of these must be true. Babson states that: "it wasn't Cade. It was Aage." . But Dabney states that: "It was Cade and it wasn't Aage."
Both of these are contradictory. so we cannot rely on them.The statements of Cade and Aage are also contradictory. So the possible solution would be Dabney.

The most simplest way to get answer is

All the wasn't statements are TRUE

Here is how I approach such problems

As you can see each person (vertically) is being accused and vindicated at the same time (hint: the green rectangle) except for $\space\textbf {Dabney}\space$ it maybe safe to assume he is the one who did at this point, but we need a solid proof not just speculations

Let's assume that $\space\textbf {Dabney}\space$ true statement was $\space\textbf {Cade}\space$ being the one who did it, that means $\space\textbf {Babson}\space$ false statement was $\space\textbf {Cade}\space$ didn't do it

That would lead to $\space\textbf {Babson}\space$ true statement will be $\space\textbf {Aage}\space$ was the one who did, which contradict the first assumption we did about $\space\textbf {Cade}\space$

$\LARGE So\space it\space has\space to\space be\space\color{#D61F06}{Dabney}$