The Λ and V are indeed very standard (although they are usually represented by U and not V, I understood their meaning).

I think you are reading too much into the problem.

(p Λ q) V ~ (p V q) = T

Is a false statement, plain and simple. It is probably just a typo or some oversight.

(p Λ q) = F
(p V q) = T
-------------
~(p V q) = F

Therefore: F V F != T

EVEN if they are saying that V is an exclusive or.