n-DNF boolean formula k satisfiability Given an n variable boolean DNF formula and a number k, does this formula has satisfying input combination greater than k?. (0&lt;=k&lt;=2^n). 
Where input is infinite number of n tuples where repeating tuple is possible.
For exampl.  F(a,b) =ab + a'b. Input set is (11,00,11,01) and k=2.
Answer is 3 here so decision says yes as 3>k.
Can i define this problem in more formal way and prove that it is np/npc/ anything else. I am looking for suggestions specially for infinite number of tuples. I am aware of npc and reduction stuffs but need help to classify this problem properly.
Your problem can't be any easier than DNF-TAUTOLOGIES since that problem is produced by setting $k$ equal to $2^n$.  Therefore your problem is NP-hard, just as DNF-TAUTOLOGIES is.