Question

Let X = {x1, x2, X3} be the set of three alternatives and AX = {(91, 92, 92) 91 +92 +93 = 1, 91,
92 93 > 0} be the set of corresponding lotteries. Moreover, letu : X-Rbe a utility function on
X and let U AX - Rbe a utility function on the set of lotteries of X
Exercise 1. (5%) Let % be the preference relation represented by U. Verify or falsify the
following statements. The preference relation % is (a) complete; (b) transitive; (c) acyclic
Exercise 2. (5%) Assume that U(1,0,0) = U(0, 0.5, 0.5).= 1 and U(0, 1, 0) = U(0.5, 0, 0.5) = 0.
Is it possible that the preference relation represented by U satisfies the independence axiom?​

Answer 1

Answer:

CORRECT ANSWER IS c

Explanation:

Correct option is

C

14.

7

C

3

Given, there are exactly three elements in A such that f(x)=y

2

..

Number of ways of selecting 3 elements from A=

7

C

3

Now the each remaining element in A can be associated with either of y

1

,y

3

in B.

Total No of ways = 2×2×2×2, but subtracting the cases where all the remaining elements getting associated to either y

1

or y

3

, we have 16−2=14 ways.

Therefore total number of onto functions = 14⋅

7

C

3