Consider the formula: (pi ^ q1) V (p2 ^ q2) V ... V (pn 1 gn)...

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Consider the formula: (pi ^ q1) V (p2 ^ q2) V ... V (pn 1 gn) where n > 2 and the p; and q; are propositional variables. This proposition has n clauses and length 4n - 1 if we count each propositional variable and operator as adding 1 to the length and we ignore the parentheses. = (A) First, write the CNF version of the proposition when n 2. Give a justification for each step. THIS SUBPROBLEM SHOULD BE SUBMITTED IN CARNAP. ONLY AN- SWERS SUBMITTED IN CARNAP WILL BE GRADED. (B) When you distribute the and over the or, what happens to the number of clauses? (C) How long is your conjunctive normal form of this formula, using the same conventions as in the problem statement? (D) For general n, how many clauses are in the conjunctive normal form as a function of n? How long is it? Consider the formula: (pi ^ q1) V (p2 ^ q2) V ... V (pn 1 gn) where n > 2 and the p; and q; are propositional variables. This proposition has n clauses and length 4n - 1 if we count each propositional variable and operator as adding 1 to the length and we ignore the parentheses. = (A) First, write the CNF version of the proposition when n 2. Give a justification for each step. THIS SUBPROBLEM SHOULD BE SUBMITTED IN CARNAP. ONLY AN- SWERS SUBMITTED IN CARNAP WILL BE GRADED. (B) When you distribute the and over the or, what happens to the number of clauses? (C) How long is your conjunctive normal form of this formula, using the same conventions as in the problem statement? (D) For general n, how many clauses are in the conjunctive normal form as a function of n? How long is it?