<user>
A: C is a truth-teller.
B: If C is a liar, then 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.
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 and C is a liar.
If C is a liar, C's statement is false, so either B is a liar and A is a liar or B is a truth-teller and A is a truth-teller or B is a liar and A is a truth-teller.
Since we know A is a liar, B must also be a liar.
Therefore, 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: C is a liar if and only if A is a liar.
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, so either C is a liar and A is a liar or C is a truth-teller and A is a truth-teller.
Since we assume A is a truth-teller, C must also be a truth-teller.
If C is a truth-teller, C's statement is true and A is a truth-teller 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, 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, so either C is a liar and A is a truth-teller or C is a truth-teller and A is a liar.
Since we know A is a liar, C must be a truth-teller.
If C is a truth-teller, C's statement is true and A is a truth-teller and B is a liar.
This contradicts the fact that A is a liar, so B must be a truth-teller.
If B is a truth-teller, B's statement is true and C is a liar and A is a liar.
This does not lead to any contradictions, so we can conclude:

CONCLUSION:
A: liar
B: truth-teller
C: liar
</assistant>
---
<user>
A: C is a liar.
B: A is a liar and C is a liar.
C: 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 C is a liar.
If C is a liar, C's statement is false and B is a truth-teller.
If B is a truth-teller, B's statement is true and A is a liar and C 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 C is a truth-teller.
If C is a truth-teller, C's statement is true and B is a liar.
If B is a liar, B's statement is false, so either A is a truth-teller or C is a truth-teller or both.
This does not lead to any contradictions, so we can conclude:

CONCLUSION:
A: liar
B: liar
C: truth-teller
</assistant>
---
<user>
A: C is a truth-teller and B is a truth-teller.
B: A is a truth-teller if and only if C is a liar.
C: B is a liar if and only if A 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 C is a truth-teller and B is a truth-teller.
If B is a truth-teller, B's statement is true, so either A is a truth-teller and C is a liar or A is a liar and C is a truth-teller.
Since we assume A is a truth-teller, C must be 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 and A is a lair or B is a truth-teller and A is a truth-teller.
Since we know A is a liar, B must be a liar.
Therefore, we can conclude:

CONCLUSION:
A: liar
B: liar
C: liar
</assistant>
---
<user>
A: If B is a truth-teller, then C is a liar.
B: A is a liar and C is a liar.
C: If B is a truth-teller, then 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, so either B is a truth-teller and C is a liar or B is a liar and C is a truth-teller or B is a liar and C is 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 liar and C 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 B is a truth-teller and C is a truth-teller.
Therefore, we can conclude:

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

CONCLUSION:
A: truth-teller
B: liar
C: liar
</assistant>
---
<user>
A: B is a truth-teller if and only if C is a truth-teller.
B: If A is a liar, then C 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, so either B is a truth-teller and C is a truth-teller or B is a liar and C is a liar.
Let's assume B is a truth-teller.
If B is a truth-teller, B's statement is true, so either A is a liar and C is a truth-teller or A is a truth-teller and C is a liar or A is a truth-teller and C is a truth-teller.
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 does not lead to any contradictions, so we can conclude:

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

CONCLUSION:
A: truth-teller
B: truth-teller
C: liar
</assistant>
