 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability/1/a/i/solution

x \in A ∖ (B \cup C)

, then

x \in A

and

x \in / B \cup C

. Thus

x \in / B

and

x \in / C

, so

x \in A ∖ B

and

x \in A ∖ C

. This proves the forward set inclusion.

Conversely, if

x \in (A ∖ B) \cap (A ∖ C)

, then

x \in A

x \in / B

, and

x \in / C

. Hence

x \in / B \cup C

x \in A ∖ (B \cup C)

. Therefore

A ∖ (B \cup C) = (A ∖ B) \cap (A ∖ C) .

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