On the island of knights and knaves you meet three natives A

On the island of knights and knaves, you meet three natives, A, B, and C, who address you
as follows:
A: At least one of us is a knave.
B: At most two of us are knaves.

What are A, B and C?

A is a knave B is a knight and C is a knave.

A and B are knights, and C is a knave.

A is a knight and B and C are knaves.

None of the above.

Solution

The correct answer is Option C i.e.

A and B are knights, and C is a knave

The best thing is to proof the solution by using the contradiction

We have assumed that A is knight, so let us equate that A = knave and we need to prove the contradiction

if we assume this statement that implies that A is lying

Hence the statement becomes there are zero knaves, but we have assumed that A is a knave

Hence a contradiction occured in our assumption, therefore we get A is a knight

Similarly prove for B = knight, assume B is knave

assuming he is lying we get all of them are knaves that is not possible since we already know that A is knight, hence we get B is also a knight

Now we have already poved two are knights, if they speak wrong then the conditions will not hold hence C must be a knave

Correct answer is Option C