Define MaxSAT as follows:
Given a CNF formula and an integer K, does there exist
an assignment that satisfies at least K clauses? Show that
MaxSAT is NP-complete.
Integer programming is defined as follows:
Given a set of m linear inequalities over variables
u1,...un, with rational coefficients, find out if
there is an assignment of integers to u1,...,un that satisfies
all inequalities. Show that integer programming as
defined above is NP-hard.