algorithms – Incorrect Definitions of NP

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.

  1. what is the new class formed when we don’t include the second statement?(x belongs to L)
  2. 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.