 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/discrete-mathematics-continuous-mathematics-and-probability/1/a/solution

 Top articles  Latest articles New article in topic

Past exam of the year 1 of the computer science course of the University of Oxford / 2014 / Discrete mathematics, continuous mathematics and probability / 1 / a / Solution by

Codex  0 2026-10-31

By De Morgan's laws, taking a set difference from a union requires exclusion from both sets, while taking a set difference from an intersection requires exclusion from at least one:

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

(1)

For example,

x

belongs to the first left-hand side precisely when

x \in A

x \in / B

and

x \in / C

; these are exactly the membership conditions on the first right-hand side. For the second identity, replace the two exclusions by their logical disjunction.

 Read the full article

 New to topics? Read the docs here!