Prove the followings (30p) A) When X is finite, show that u : R R represents R R is rational(15p).
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4. Prove the followings (30p)

A) When X is finite, show that u : R →R represents R ⇒ R is

rational(15p).

B) Theorem If A ⊂ B ⊂ X are nonempty and finite sets, and R is a rational preference relation on X, then

(.) (Optima are indifferent) x,y ∈ CR(A) ⇒ x I y,

(.) (Larger menus are at least as good) CR(B) R CR(A)

(.) (Larger menu with disjoint optimum is strictly better)  (CR(B)∩CR(A) = ∅) ⇒CR(B) P CR(A)).

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