 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2010/e/e3/b/ii/solution

K_{a} \cap K_{b} \neq = \emptyset

, their union is connected by (a)(iii). It contains

a

, so maximality gives

K_{a} \cup K_{b} \subseteq K_{a}

and hence

K_{b} \subseteq K_{a}

. Interchanging the roles gives the reverse inclusion. Thus the two components coincide; otherwise they are disjoint.

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