 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/discrete-mathematics-continuous-mathematics-and-probability-resit/1/c/iii/solution

The commutativity and associativity of set intersection give

(A ∖ B) ∖ C = A \cap B^{c} \cap C^{c} = A \cap C^{c} \cap B^{c} = (A ∖ C) ∖ B .

Equivalently, part (ii) reduces both sides to removal of the same set union

B \cup C = C \cup B

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