Determine whether true or false then negate

a) For every A is an element of P(N) (A does npt =0 or for some a is an element of A(a+1 is an element of N/A))

b) for every k is an element of N for some S is an element of P({1,...,k})(S= S^c)

c) For every k is an element of N For some S is an element of P({1,...,k}) Fpr every b is an element of {1,...,k}(b is an element of S or b + 1 is an element of S)