### Artificial IntelligenceAIMA Exercises

Prove each of the following assertions:
1. Every pair of propositional clauses either has no resolvents, or all their resolvents are logically equivalent.
2. There is no clause that, when resolved with itself, yields (after factoring) the clause $(\lnot P \lor \lnot Q)$.
3. If a propositional clause $C$ can be resolved with a copy of itself, it must be logically equivalent to $True$.

Prove each of the following assertions:
1. Every pair of propositional clauses either has no resolvents, or all their resolvents are logically equivalent.
2. There is no clause that, when resolved with itself, yields (after factoring) the clause $(\lnot P \lor \lnot Q)$.
3. If a propositional clause $C$ can be resolved with a copy of itself, it must be logically equivalent to $True$.

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