This topic is from book logic for Computer science by Gallier,Please solve with all the required steps, This topic is related to Propositional Logic Gentzen System G^{' ,}

For each of the following propositional formulas A, construct a propo sitional formula B in conjunctive normal form and a counterexample tree of G' such that the counterexample tree shows A and B are logi- cally equivalent (see Example 3.4.5 in Gallier 2015): For each of the following propositional formulas A, construct a propo sitional formula B in conjunctive normal form and a counterexample tree of G' such that the counterexample tree shows A and B are logi- cally equivalent (see Example 3.4.5 in Gallier 2015)