3. [16 marks] 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. Here is a list of five propositional forms and three circuits. This list (A) p (qr). (B) q(pr). (C) (pAq)+(q V r). (D) ~(~pVr)(r ^ q). (E) (pr) ^ (~r(q V~p)) (F) output (G) P output (H) 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 ry = ~IVy and that rey = (r V y) A~(I^y) = (~IAy) V (xA~y)). 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