A complete "truth table" for the "DOORS" problem requires a rather lengthy construction, and since it's 3-dimensional, is a little tough to describe in text.

Assume that door A is GOOD.
Assume Angel 1 is TRUE
Assume angel 2 is FALSE

If you ask Angel 1 "Is door A the way to Heaven?" he will answer YES.
If you ask Angel 2 "Is door A the way to Heaven?" he will answer NO.

If you ask Angel 1 "Would your brother say door A is the way to heaven?"
Brother Angel 2 is a liar so he would say "NO," and Angel 1 tells the truth so the answer is "NO"

If you as Angel 2 "Would your brother say door A is the way to heaven?"
Angel 1 would tell the truth, and would answer "YES" but Angel 2 lies so he would say "NO"

Repeat for door A is GOOD
Angel 1 is FALSE
Angel 2 is TRUE

Repeat for door A is BAD
Angel 1 is TRUE
Angel 2 is FALSE

Repeat for door A is BAD
Angel 1 is FALSE
Angel 2 is TRUE

In every case, when you ask either angel "Would your brother say Door A is the way to Heaven?" a "NO" reply means door A is the way to heaven and a "YES" answer means that it is NOT.

(Attempts to introduce artificial postulates and possibilities (even when the question is only partially formed in the original statement) merely indicates a reply from someone not really interested in the logic. This is a well known, and not totally trite, classic of formal logic.

John