

Prove each of the following assertions:<br>

1.  Every pair of propositional clauses either has no resolvents, or all
    their resolvents are logically equivalent.<br>

2.  There is no clause that, when resolved with itself, yields
    (after factoring) the clause $(\lnot P \lor \lnot Q)$.<br>

3.  If a propositional clause $C$ can be resolved with a copy of itself,
    it must be logically equivalent to $ True $.<br>
