Answer the following conceptual questions based on the axioms of probability.
a. Prove that P(∅)=0 for every probability function P defined on a sample space S.
b. Show that if B⊆A⊆S, then P(B)≤P(A).
c. Give a brief explanation, using the axioms, of why a value such as −0.2 cannot represent the probability of any event.