Please answer all parts. Thanks in advance!

Problem 1 In this problem you'll play around with some of the concept classes we discussed in class (and some of their close friends). (i) Let S be a subset of {1,..., n}. The parity function corresponding to S is the Boolean function f:{0,1}" + {0,1}, f(t1, ..., In) = ri mod 2 ies which counts whether the number of input bits in coordinates indexed by S is odd or even. True or false: For every SC [n], the parity function corresponding to S is computed by a poly(n)- term DNF. (Justify your answer.) (ii) A concept c: {0,1}" + {0,1} is said to be monotone if whenever two inputs r, y = {0,1}" satisfy I