An instance of the problem AlmostSAT is a CNF Boolean formula containing at least 2 clauses, plus the index number of a

[answerhappygod]

An instance of the problem AlmostSAT is a CNF Boolean formula
containing at least 2 clauses, plus the index number of a clause in
that formula. For example an instance of AlmostSAT could be
represented as:
'(X2 OR X3) AND (NOT X3) AND (NOT X2);1'
A positive instance is one in which there is a variable
assignment that satisfies all the clauses, except possibly the one
specified by the index number. The example above is a positive
instance of AlmostSAT because '(X2 OR X3) AND (NOT X2)' can be
satisfied by setting X2 to False and X3 to True.
Like SAT, a positive instance of SAT¬ℇ is
a satisfiable CNF Boolean formula. The only difference is that an
instance of SAT¬ℇ must contain at least one clause.
Prove that AlmostSAT and
SAT¬ℇ are polyequivalent.
That is, prove that AlmostSAT ≤p
SAT¬ℇ, and that
SAT¬ℇ ≤
AlmostSAT. (Show that positive instances can be
mapped to positive instances, negative to negative.)