 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability-resit/1/d/solution

Put

B = T \cap S

g (A) = B \cup (T \cap A)

and

B \subseteq T

. Consequently,

g (g (A)) = B \cup (T \cap (B \cup (T \cap A))) = B \cup (T \cap B) \cup (T \cap A) = B \cup (T \cap A) = g (A) .

A \in P (U)

, so $g \circ g = g$ :

g

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