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 = NP), (a) Consider the language TAUT-p I is a tautology} ie. the set of all boolean formulas E (b) It is currently unknown whether coNPNP (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 coNP unequal). For example, TAUT is in coNP but is not known or thought to be in NP. Why (c) We could analogously define cof- 1 L E P}, however this is not a particularly useful (d) One way of proving that PNP 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 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 = NP), (a) Consider the language TAUT-p I is a tautology} ie. the set of all boolean formulas E (b) It is currently unknown whether coNPNP (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 coNP unequal). For example, TAUT is in coNP but is not known or thought to be in NP. Why (c) We could analogously define cof- 1 L E P}, however this is not a particularly useful (d) One way of proving that PNP 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