Consider the following four students who make choices from subsets of S = {a, b, c}.

(a) Student 1s choice are given by c1({a, b, c}) = {a, b}, c1({a, b}) = {a, b}, c1({a, c}) = {a} , c1({b, c}) = {b}. Does she satisfy Sens property ? Does she satisfy Sens property ? Explain your reasoning.

(b) Student 2s choices are given by c2({a, b, c}) = {a, b}, c2({a, b}) = {a, b}, c2({a, c}) = {a, c} , c2({b, c}) = {b}. Does she satisfy Sens property ? Does she satisfy Sens property ? Explain your reasoning.

(c) Student 3s choices are given by c3({a, b, c}) = {b}, c3({a, b}) = {b}, c3({a, c}) = {a, c} , c3({b, c}) = {b}. Does she satisfy Sens property ? Does she satisfy Sens property ? Explain your reasoning.

(d) Student 4s choices are given by c4({a, b, c}) = {a, b}, c4({a, b}) = {a}, c4({a, c}) = {a} , c4({b, c}) = {b}. Does she satisfy Sens property ? Does she satisfy Sens property ? Explain your reasoning.

(e) For each these four students, (i) explain if she can be modeled as maximizing a payoff function and if so, (ii) present such a payoff function.