I was solving problems related to P and NP where I encountered the following problem:

Given a standard definition of NP,

if x belongs to L then there exists y such that |y| <= |x|^d and A(x, y) = 1;

if x does not belong to L then for every y with |y| <= |x|^d we have A(x, y) = 0.

- what is the new class formed when we don’t include the second statement?(x belongs to L)
- what is the new class formed when we don’t include the first statement? (x does not belong to L)

I am well versed with the definitions of P and NP but unable to figure out how to determine and prove these new classes.