4. (10 pt) [01,02] We call a set of connectives adequate if the connectives in the set are sufficient to express every possible propositional formula. It is easy to see that S = {-, V, A} is an adequate set of connectives, because every possible propositional formula corresponds to a truth table and the truth table can be uniquely represented in DNF which consists of only connective -, V, and A. (a) Please prove that P = {-, V} is an adequate set of connectives. (Hint: to prove a set is adequate, it is sufficient to prove that we can use the connectives in the set to replace all connectives in another adequate set.) (b) Define a connective t. For any proposition p and q, p t q takes value true if and only if p and q are both true. Please prove or disprove that Q = {1} is adequate. (c) Define a connective J. For any proposition p and q, p | q takes value true if and only if p and q are both false. Please prove or disprove that R = {{} is adequate