Which of the following statements illustrates a counterexample proving that the propositions ∃x(p(x) ∧ q(x)) and ∃xp(x)∧∃xq(x) are not logically equivalent?
a) For all x, p(x) is true and q(x) is false.
b) There exists an x such that p(x) is true and q(x) is false.
c) There exists an x such that p(x) is false and q(x) is true.
d) For all x, p(x) is false and q(x) is true.