Knights always tell truth Knaves always lies Identify who is

Knights always tell truth, Knaves always lies (Identify who is a knight and who is a knave)

A tells (one of us is a knight OR one of us is a knave)    B tells (A is correct)

A tells (one of us is a knight OR one of us is a knave)    B tells (A is not correct)

A tells (one of us is a knight AND one of us is a knave)    B tells (A is correct)

A tells (one of us is a knight AND one of us is a knave)    B tells (A is not correct)

Solution

A has made 2 statements:

1. one of us is a knight OR one of us is a knave   

2. one of us is a knight AND one of us is a knave

Each of the above statements was made twice. Once the response of B was \"A is correct\" and the second time, to the same statement, B\'s response was \" A is not correct\". One of these 2 responses is apparently False and the other True. Hence, B cannot be the Knight as Knights always tell truth. B also cannot be the Knave as Knaves always lie. Similarly, A has made 2 different statements, of which, only one is True. Hence A also cannot be either a Knight or a Knave.