Consider the following lotteries: 

• L₁ = [1, 1]. 

• L₂ = [0.5, 2; 0.5, 0]. 

• L₃ = [1, 2].

Four students have expressed their preferences over these lotteries as follows: 

• Adam is indifferent between lottery L₂ and lottery L₁. 

• Becky prefers lottery L₁ to lottery L₂. 

• Charles is indifferent between lottery L₃ and lottery L₂. 

• Diana prefers lottery L₂ to lottery L₁.

Match each student with a utility function that is consistent with their stated preferences. Each student has a different utility function. 

a. Which student has the utility function of U(x) = x² 

b. Which student has the utility function of U(x) = x 

c. Which student has the utility function of U(x) = √ x 

d. Which student has the utility function of none of the ones above