Aproposition is in conjunctive normal form (cnf) if it consists of the conjunction of a finite number of propositions, each of which is a disjunction formed from a finite number of simple propositions (i. e., variables) p1,p2, .. , рn. so, for eхample, (pi v p3 v -ре) л (p1 v -рз) л (р5 v p> ) is in cnf: it consists of the conjunction of three clauses, and each of these is formed by taking the disjunction of a number of the variables or their negations. note that in cnf, the negation of a variable, such as with "p5) is allowed, but that the negation of a compound proposition -( v p2) is not theorem: every compound proposition formed from -, v, a, -», and > is logically equivalent to a proposition in cnf this theorem is really nice because it means you can assume your proposition is of this form without losing any generality. this is convenient, in particular, when working with applications problems concerned with determining whether a proposition in cnf has a truth set: is there any assignment of truth values to the variables that makes the entire expression true? any such assignment satisfies the proposition. a special of this problem, known as 3-sat is known to be provably difficult in general (it is "np-complete"). (a) convert -1) ar) to cnf using logical equivalences. make sure to justify every step! (b) find an on computers. anyway, there's an important class of nonempty case assignment of truth values that satisfies (рi v p3) ^ (рі v-p3 v pa v p5)л (~рә) л (р2 v ps).