<user>
A: B is a liar.
B: E is a truth-teller and D is a liar.
C: If B is a liar, then D is a liar.
D: If E is a liar, then B is a liar.
E: If D is a liar, then C is a liar.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller. The statement of A must be true. So B is a liar.
B is a liar, at least one of B's statements must be false. Either E is a liar or D is a truth-teller or E is a liar and D is a truth-teller.
Let's assume E is a liar.
If E is a liar, the statement of E must be a lie. So D must be a liar and C must be a truth-teller.
If E is a liar and B is a liar, the statement of D is true. So D must be a truth-teller. 
This contradicts our assumption that E is a liar and therefore D is a liar.
Therefore, if A is a truth-teller, E must be a truth-teller and D must also be a truth-teller.
If D is a truth-teller, the statement of B about D is false. So B must be a liar.
If B is a liar and D is a truth-teller, the statement of C is false. So C must be a liar.
This does not lead to any contradictions. Therefore we can conclude:

CONCLUSION:
A: truth-teller
B: liar
C: liar
D: truth-teller
E: truth-teller
</assistant>
---
<user>
A: If C is a liar, then E is a liar.
B: E is a truth-teller.
C: B is a truth-teller if and only if D is a truth-teller.
D: If C is a liar, then E is a liar.
E: If D is a truth-teller, then B is a liar.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, then the statement of A must be true. Either C is a truth-teller and we know nothing about E based on the statement of A, or C and E are both liars.
Let's assume C is a truth-teller.
If C is a truth-teller, the statement of D about C is true. So D must be a truth-teller.
If C is a truth-teller, then the statement of C must be true. B and D are either both truth-tellers or liars.
Since D is a truth-teller, B must be a truth-teller.
If B is a truth-teller, the statement of B must be true. So E is a truth-teller.
Since D is a truth-teller and B is a truth-teller, the statement of E is false. So E is a liar.
This leads to a contradiction. Therefore, if A is a truth-teller, C can not be a truth-teller, C and E must be both liars.
If E is a liar, the statement of B about E is false. So B is a liar.
If C is a liar and E is a liar, the statement of D is true, so D is a truth-teller.
If B is a liar and D is a truth-teller, the statement of E is true, so E must be a truth-teller.
This contradicts our assumption that A is a truth-teller and therefore E is a liar.
So A must be a liar.
If A is a liar, the statement of A must be false. So C must be a liar and E must be a truth-teller.
If E is a truth-teller, the statement of B about E is true. So B is a truth-teller.
If C is a liar and E is a truth-teller, the statement of D is false, so D is a liar.
Therefore we can conclude:

CONCLUSION:
A: liar
B: truth-teller
C: liar
D: liar
E: truth-teller
</assistant>
---
<user>
A: If E is a liar, then B is a truth-teller.
B: D is a truth-teller and A is a liar.
C: D is a truth-teller if and only if E is a truth-teller.
D: If A is a truth-teller, then E is a truth-teller.
E: A is a truth-teller and C is a truth-teller.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, the statement of A must be true. Either E is a truth-teller and we know nothing about B based on the statement of A, or E is a liar and B is a truth-teller.
Let's assume E is a truth-teller.
If A and E are both truth-tellers, the statement of D is true. So D is a truth-teller.
If D and E are both truth-tellers, the statement of C is true. So C is a truth-teller.
If D and A are both truth-tellers, the statement of B is false. So B is a liar.
This does not lead to any contradictions. Therefore we can conclude:

CONCLUSION:
A: truth-teller
B: liar
C: truth-teller
D: truth-teller
E: truth-teller
</assistant>
---
<user>
A: C is a truth-teller.
B: If E is a liar, then A is a truth-teller.
C: If B is a liar, then A is a liar.
D: If A is a truth-teller, then C is a liar.
E: A is a truth-teller and C is a liar.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, the statement of A must be true. So C is a truth-teller.
If A is a truth-teller and C is a truth-teller, the statement of E is false. So E is a liar.
If A is a truth-teller and C is a truth-teller, the statement of D is false. So D is a liar.
If E is a liar and A is a truth-teller, the statement of B is true. So B is a truth-teller.
This does not lead to any contradictions. Therefore we can conclude:

CONCLUSION:
A: truth-teller
B: truth-teller
C: truth-teller
D: liar
E: liar
</assistant>
---
<user>
A: D is a truth-teller if and only if C is a liar.
B: E is a liar.
C: B is a truth-teller.
D: B is a liar.
E: D is a liar if and only if B is a truth-teller.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller. The statement of A must be true. Either D is a truth-teller and C is a liar, or D is a liar and C is a truth-teller.
Let's asusme D is a truth-teller and C is a liar.
If C is a liar, the statement of C must be false. So B must be a liar.
If B is a liar, the statement of D is true, so D must be a truth-teller.
This leads to no contradictions so far.
If D is a truth-teller and B is a liar, the statement of E is true. So E is a truth-teller.
Therefore we can conclude:

CONCLUSION:
A: truth-teller
B: liar
C: liar
D: truth-teller
E: truth-teller
</assistant>
---
<user>
A: B is a truth-teller if and only if C is a truth-teller.
B: D is a liar and A is a truth-teller.
C: A is a liar.
D: C is a truth-teller and A is a liar.
E: C is a truth-teller.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, the statement of C about A is false. So C is a liar.
If A is a truth-teller, the statement of A must be true. B and C are either both truth-tellers or both liars.
We know if A is a truth-teller, then C is a liar, B must also be a liar.
If A is a truth-teller and C is a liar, the statement of D is false, so D is a liar.
If D is a liar and A is a truth-teller, the statement of B is a true. B is a truth-teller.
This contradicts our assumption that A is truth-teller and therefore B is a liar.
So A must be a liar.
If A is a liar, the statement of C about A is true. C is a truth-teller.
If C is a truth-teller and the statement of A is true, then B is a liar.
If C is a truth-teller, then the statement of E about C is true. So E is a truth-teller.
If C is a truth-teller and A is a liar, the statement of D is true. So D is a truth-teller.
Therefore we can conclude:

CONCLUSION:
A: liar
B: liar
C: truth-teller
D: truth-teller
E: truth-teller
</assistant>
---
<user>
A: D is a liar and B is a liar.
B: A is a truth-teller if and only if C is a liar.
C: If A is a truth-teller, then E is a liar.
D: If A is a liar, then B is a liar.
E: D is a liar and A is a liar.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, the statement of D is true. So D is a truth-teller.
If A is a truth-teller, the statements of A must be true. So D is a liar and B is a liar.
This contradicts our assumption that A is a truth-teller and therefore D is a truth-teller.
So A must be a liar.
A is a liar, so at least one of A's statements must be false. Either D is a truth-teller or B is a truth-teller or they are both truth-tellers.
Let's assume B is a truth-teller.
If B is a truth-teller, the statement of B must be true. We know A is a liar, then C must be a truth-teller.
If A is a liar and B is a truth-teller, then the statement of D is false. So D must be a liar.
If D is a liar and A is a liar, the statement of E is true. So E is a truth-teller.
This does not lead to any contradictions. Therefore we can conclude:

CONCLUSION:
A: liar
B: truth-teller
C: truth-teller
D: liar
E: truth-teller
</assistant>
---
<user>
A: D is a truth-teller.
B: A is a truth-teller and C is a liar.
C: If E is a truth-teller, then A is a liar.
D: If C is a liar, then B is a truth-teller.
E: A is a liar and D is a liar.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, the statement of A must be true. So D is a truth-teller.
If A is a truth-teller, the statement of E about A is false. So E is a liar.
If E is a liar, the statement of C is true. So C is a truth-teller.
If C is a truth-teller, the statement of B is false. So B is a liar.
This does not lead to any contradictions. Therefore we can conclude:

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