<user>
A: B is a liar.
B: C is a liar.
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 that B is a liar is true.
If B is a liar, B's statement that C is a liar is false.
If C is a truth-teller, all of C's statements are true, so A is a truth-teller and B is a truth-teller.
This leads to a contradiction, since we assume B is a liar.
Therefore A can not be a truth-teller and must be a liar.
If A is a liar, A's statement that B is a liar is false, therefore B must be a truth-teller.
If B is a truth-teller, B's statement that C is a liar must be true.
If C is a liar, C's statement must be false, so either A is a liar, or B is a liar or both are liars.
This does not lead to a contradiction, so we can conclude:

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

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

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

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

CONCLUSION:
A: liar
B: truth-teller
C: liar
</assistant>
---
<user>
A: If C is a liar, then B is a liar.
B: C is a liar.
C: A is a liar and B is a liar.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, then A's statement must be true, so either C 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 liar, then A's statement can only be true if C is a truth-teller.
If C is a truth-teller, then C's statement is true, so A is a liar and B is a liar.
This contradicts the assumption that A is a truth-teller.
If A is a liar, then A's statement must be false, so C must be a liar and B must be a truth-teller.
If C is a liar, then C's statement must be false, so either A is a truth-teller or B is a truth-teller or both.
If B is a truth-teller, then B's statement must be true, so C must be a liar.
There are no contradictions, so we can conclude:

CONCLUSION:
A: liar
B: truth-teller
C: liar
</assistant>
---
<user>
A: B is a truth-teller and C is a truth-teller.
B: C is a liar.
C: A is a truth-teller.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, then A's statement must be true, so B must be a truth-teller and C must be a truth-teller.
If B is a truth-teller, then C must be a liar. However, this contradicts with A's statement that B and C are both truth-teller.
This leads to a contradiction for A, therefore A can not be a truth-teller.
If A is a liar, then A's statement must be false, so either B must be a liar and C a truth-teller, or C must be a liar or B a truth-teller, or both B and C are liars.
Since we know A is a liar, C's statement that A is a truth-teller is false, and C must be a liar.
Since B is stating that C is a liar, B must be a truth-teller.
This does not lead to any contradictions, so we can conclude:

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