Question: Which of the following utility fuctions have the expected utility property?

a) \[u\left( {{c}_{1}},{{c}_{2}},{{\pi }_{1}},{{\pi }_{2}} \right)=a\left( {{\pi }_{1}}{{c}_{1}}+{{\pi }_{2}}{{c}_{2}} \right)\]

b) \[u\left( {{c}_{1}},{{c}_{2}},{{\pi }_{1}},{{\pi }_{2}} \right)={{\pi }_{1}}{{c}_{1}}+{{\pi }_{2}}c_{2}^{2}\]

c) \[u\left( {{c}_{1}},{{c}_{2}},{{\pi }_{1}},{{\pi }_{2}} \right)={{\pi }_{1}}\ln {{c}_{1}}+{{\pi }_{2}}\ln {{c}_{2}}+17\]