Here is a list of five propositional forms and three circuits. This list contains four pairs of logically equivalent entries (we will say a circuit is equivalent to a propositional form if the propositional form describes the value of the circuit's output for all possible combinations of input values). For instance, maybe A = B, C =D, E=F and G =H). First determine the four pairs, and then prove for each pair that one element of the pair is logically equivalent to the other one. (A) P+(q+r). (B) +( +r). (C) (paq) +(Vr). (D) ~(~Vr) +(). (E) (p+r)^(+qVp) output @@ @ @ @ @ @ @ @ output output You are allowed to use truth tables to figure out the equivalences; however at least three of your proofs must use a sequence of known logical equivalences (see Epp 5 or Epp-4 table 2.1.1, Epp-3 table 1.1.1, Rosen-6 table 6 in section 1.2, Rosen-7 table 6 in section 1.3, or Dave's excellent formula sheet; you can also assume that I +y = - Vy and that rey = r Vy) A 1 Ay) = ( Ay) V (Ay ). The fourth proof can use either a sequence of known logical equivalences, or a truth table. Hint: you might want to translate the circuits into formulas that mirror exactly as the circuit is implemented, before using any logical equivalence rules