Working on logic. I think understanding 'or' to mean 'union', 'and' to be 'intersection' and 'xor' as it is, this become a lot less confusing.

I wanted, basically, to give xor for two circle in three, so I had to admit c using the "implies" operator.

((A xor B ) and not C) or (B xor C and not A) = (A and B and C) xor A xor B xor C

or

((A xor B) and not C) or (B xor C and not A) = (A and B and C) xor A xor B xor C (Translated by Bing)