6. Conceptually, NP represents the class of decision problems whose "yes" answers can be ver ified efficiently. In this problem, we will consider its counterpart: coNP =1 L e NP), (a) Consider the language TAUTS: { is a tautology) i.e. the set of all boolean formulas E (b) It is currently unknown whether coNP NP (though they are widely believed to be representing the set of decision problems whose "no" answers are efficiently verifiable that are satisfied by all assignments. Show that TAUT E CONP. unequal). For example, TAUT is in coNP but is not known or thought to be in NP. Why (c) We could analogously define coP (LILE P), however this is not a particularly useful (d) One way of proving that P NP would be to prove that NPcoNP. Show that might it be difficult to construct an efficient verifier for TaUT? class. Show that P coP; that is, show that P is closed under complement