2. [20 marks] Here is a list of 5 propositional forms and 3 circuits. This list contains 4 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) (pq) r. (B)~PV (r q). (C) ~ (~ (p ^ q) V ~ (g ^r)) (D) (r^ p) (r^g). (E) (qp) ^ (~pr) ^ (~qr) (F) (G) (H) 9 q a TH You are not allowed to use truth tables to prove the equivalences, but you are free to use them to match the pairs (you don't need to add them to your solution). All your proofs must use a sequence of known logical equivalences.