Prove that STINGY SAT is NP-complete

Problem:

STINGY SAT is the following problem:given a set of clauses(each a disjunction of literals) and an interger k, find a satisfying assignment in which at most k variables are true, if such an assignment exists. Prove that STINGY SAT is NP-complete.

Solution:

设SAT一个为I，并且此时的变量数量为K，那么该SAT的解中满足不超过K个变量为真，则转化为了STINGY SAT问题，I的解也为STINGY SAT的解，因为SAT为NP-complete，所以STINGY SAT也是NP-complete。