How can I solve this problem by using duality? like dual (x V y) = dual (x) ^ dual(y)

In lectures it was discussed how to convert a formula q into CNF. The procedure was described as follows: 1. Compute an equivalent DNF, 41, for -p. 2. Let 12 be the dual of 11 (replace / with V and vice-versa, and T with 1 and vice-versa). 3. Let 1/3 be the result of replacing, in 12, all literals with their negations (replace p with -p and -p with p). This will be a formula in CNF that is equivalent to q. Suppose F denotes the set of well-formed formulas over PROP. We can formally define the last step as 13 = flip(12) where flip : F - F, is recursively defined as follows: . flip ( T) = T . flip ( 1 ) = 1 . flip(p) = -p for all p E PROP . flip(-p) = p for all p E PROP. flip(-q) = -flip(q) for all formulas q which are not propositional variables . For all formulas q and y: - flip ((9 / 4) ) = (flip(4) A flip(up) ) - flip ((Q V 4) ) = (flip(Q) V flip(4) ) - flip ((9 -+ 1)) = (flip() - flip(1) ) - flip ((9 1)) = (flip(q) flip(4) ) (a) Recursively define a function dual : F - F so that the last two steps above process can be formally defined as flip o dual (1)1). (4 marks) (b) Prove that if u is in DNF then flip o dual (up ) is in CNF. (4 marks) (c) Prove that for all q E F, flip o dual (-) is logically equivalent to q. (6 marks)