text: 
  
  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>
  