Different Classes 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| &lt;= |x|^d and A(x, y) = 1;
if x does not belong to L then for every y with |y| &lt;= |x|^d we have A(x, y) = 0.

1. what is the new class formed when we don't include the second statement?
2. what is the new class formed when we don't include the first statement?
I am well versed with the definitions of P and NP but unable to figure out how to determine these new classes.
 Any help in understanding these concepts would be appreciated.
Here is a big hint to help you solve the problem:

 Can you give an example of a language that is in this class?  Can you give an example of a language that is not in this class?