<user>
A: B is a truth-teller.
B: A is a truth-teller and C is a liar.
C: B is a truth-teller.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and B is a truth-teller.
If B is a truth-teller, B's statement is true and A is a truth-teller and C is a liar.
If C is a liar, C's statement is false and B is a liar.
This leads to a contradiction, so A cannot be a truth-teller.
If A is a liar, A's statement is false and B is a liar.
If B is a liar, B's statement is false and either A is a liar or C is a truth-teller or both.
Since we know A is a liar, this does not lead to a contradiction.
Let's assume C is a truth-teller.
If C is a truth-teller, C's statement is true and B is a truth-teller.
This leads to a contradiction, since we know B is a liar.
Therefore, C must be a liar and we conclude:

CONCLUSION:
A: liar
B: liar
C: liar
</assistant>
---
<user>
A: B is a liar and C is a liar.
B: A is a truth-teller.
C: I am a truth-teller.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and B is a liar and C is a liar.
If B is a liar, B's statement is false and A is a liar.
This leads to a contradiction, so A must be a liar.
If A is a liar, A's statement is false, so either B is a truth-teller or C is a truth-teller or both.
Let's assume B is a truth-teller.
If B is a truth-teller, B's statement is true and A is a liar.
This leads to a contradiction, so B must be a liar.
Since we know B is a liar and A's statement is false, C must be a truth-teller.
Therefore, we conclude:

CONCLUSION:
A: liar
B: liar
C: truth-teller
</assistant>
---
<user>
A: B is a truth-teller and C is a truth-teller.
B: A is a truth-teller and C is a truth-teller.
C: A is a truth-teller and B is a liar.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and B is a truth-teller and C is a truth-teller.
If B is a truth-teller, B's statement is true and C is a truth-teller.
If C is a truth-teller, C's statement is true and B is a liar.
This leads to a contradiction, so A must be a liar.
If A is a liar, A's statement is false and either B is a liar or C is a liar or both.
Let's assume B is a liar.
If B is a liar, B's statement is false, so either A is a liar or C is a liar or both.
Since we know A is a liar, this does not lead to a contradiction.
Let's assume C is a liar.
If C is a liar, C's statement is false, so either A is a liar or B is a truth-teller or both.
Since we know A is a liar, this does not lead to a contradiction.
Therefore, we can conclude:

CONCLUSION:
A: liar
B: liar
C: liar
</assistant>
---
<user>
A: B is a truth-teller and C is a liar.
B: C is a liar.
C: B is a truth-teller and A is a liar.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and B is a truth-teller and C is a liar.
If B is a truth-teller, B's statement is true and C is a liar.
If C is a liar, C's statement is false, so either B is a liar or A is a truth-teller or both.
Since we know A is a truth-teller, this does not lead to a contradiction.
Therefore, we can conclude:

CONCLUSION:
A: truth-teller
B: truth-teller
C: liar
</assistant>
---
<user>
A: C is a truth-teller and B is a truth-teller.
B: A is a truth-teller.
C: B is a truth-teller and A is a liar.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and C is a truth-teller and B is a truth-teller.
If C is a truth-teller, C's statement is true and B is a truth-teller and A is a liar.
This leads to a contradiction, so A must be a liar.
If A is a liar, A's statement is false, so either C is a liar or B is a liar or both.
Let's assume C is a liar.
If C is a liar, C's statement is false, so either B is a liar or A is a truth-teller or both.
Let's assume B is a liar.
If B is a liar, B's statement is false and A is a liar.
This does not lead to a contradiction, therefore we can conclude:

CONCLUSION:
A: liar
B: liar
C: liar
</assistant>
---
<user>
A: B is a liar and C is a truth-teller.
B: A is a truth-teller and C is a liar.
C: B is a truth-teller.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and B is a liar and C is a truth-teller.
If B is a liar, B's statement is false, so either A is a liar or C is a truth-teller or both.
If C is a truth-teller, C's statement is true and B is a truth-teller.
This leads to a contradiction, so A must be a liar.
If A is a liar, A's statement is false, so either B is a truth-teller or C is a liar or both.
Let's assume B is a truth-teller.
If B is a truth-teller, B's statement is true and A is a truth-teller and C is a liar.
Since we know A is a liar, this leads to a contradiction, so B must be a liar.
If B is a liar, B's statement is false, so either A is a liar or C is a truth-teller or both.
This does not lead to a contradiction.
If C is a liar, C's statement is false and B is a liar.
This does not lead to a contradiction, so we can conclude:

CONCLUSION:
A: liar
B: liar
C: liar
</assistant>
---
<user>
A: B is a truth-teller and C is a truth-teller.
B: I am a truth-teller.
C: B is a truth-teller and A is a liar.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and B is a truth-teller and C is a truth-teller.
If B is a truth-teller, B's statement is true and A is a truth-teller.
If C is a truth-teller, C's statement is true and B is a truth-teller and A is a liar.
This leads to a contradiction, so A must be a liar.
If A is a liar, A's statement is false, so either B is a liar or C is a liar or both.
Let's assume B is a liar.
If B is a liar, B's statement is false and B is a liar.
Let's assume C is a liar.
If C is a liar, C's statement is false, so either B is a liar or A is a truth-teller or both.
Since we know B is a liar, this does not lead to a contradiction.
Therefore, we can conclude:

CONCLUSION:
A: liar
B: liar
C: liar
</assistant>
---
<user>
A: I am a truth-teller.
B: C is a liar and A is a truth-teller.
C: A is a truth-teller and B is a truth-teller.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and A is a truth-teller.
If B is a truth-teller, B's statement is true and C is a liar and A is a truth-teller.
If C is a liar, C's statement is false, so either A is a liar or B is a liar or both.
This leads to a contradiction, so A must be a liar.
Let's assume B is a truth-teller.
If B is a truth-teller, B's statement is true and A is a truth-teller and C is a liar.
Since we know A is a liar, this leads to a contradiction, so B must be a liar.
If B is a liar, B's statement is false, so either C is a truth-teller or A is a liar or both.
Let's assume C is a truth-teller.
If C is a truth-teller, C's statement is true and A is a truth-teller and B is a truth-teller.
This leads to a contradiction, so C must be a liar.
Therefore, we can conclude:

CONCLUSION:
A: liar
B: liar
C: liar
</assistant>
