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 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:For example, $x$ belongs to the first left-hand side precisely when $x\in A$, $x\notin B$ and $x\notin C$; these are exactly the membership conditions on the first right-hand side. For the second identity, replace the two exclusions by their logical disjunction.