Let the negation of a≠ 1 or b≠2 be a proposition: a =1,B = 2；;

The negation of a+b≠3 is the proposition B: A+B = 3.

Obviously, a is a necessary and sufficient condition for b,

Therefore, a≠ 1 or b≠2 is a necessary and sufficient condition for a+b≠3. Choose B.

This problem is judged from its negative proposition first.