If D = fn + (p x 0) then AD = - fn - (p x 0)
Don't you have to tidy it up a bit?
IF D = fn + 0p THEN AD = - fn - 0p
IF D = fn THEN AD = - fn
or the reciprocal of AD is fn
1/AD = fn
Therefore AD = 1/fn
Which implies that D or fn/1 = 1/fn or AD
Therefore fn is either -1 or 1.
So yes or no.
Or in this case, DOOM or NOT DOOM.
It's a long time since I did Maths.
My head hurts.