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 = {L | L NP), representing the set of decision problems whose "no" answers are efficiently verifiable. (a) Consider the language TAUT = { I is a tautology) i.e. the set of all boolean formulas that are satisfied by all assignments. Show that TAUT coNP (b) It is currently unknown whether coNP NP (though they are widely believed to be unequal). For example. TAUT is in coNP but is not known or thought to be in NP. Why 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. NP CoNPP NP. (c) We could analogously define coP LILE P), however this is not a particularly useful (d) One way of proving that PNP would be to prove that NPcoNP. Show that