Question: (a) Prove the equivalence (5.25), including the inequalities, for real numbers (A, B, C) that fulfill (A

(a) Prove the equivalence (5.25), including the inequalities, for real numbers $A, B, C$ that fulfill \(A

(b) Prove $(1-\alpha) \mathbb{E}(u, P)+\alpha \mathbb{E}(u, R)=\mathbb{E}(u,(1-\alpha) P+\alpha R)$ for two lotteries $P$ and $R$, which is the second equation in (5.30).

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