Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Discrete mathematics, continuous mathematics and probability resit / 1 / a

Let $A$ and $B$ be the finite sets of objects satisfying the two properties. The rule of sum says that mutually exclusive alternatives have additive counts: if $A\cap B=\varnothing$, then $|A\cup B|=|A|+|B|$. Without disjointness, the corresponding inclusion-exclusion principle isThe rule of subtraction counts objects satisfying the first property but not the second:In particular, if the objects with the second property form a subset of those with the first, the count is $|A|-|B|$. These conditions prevent either double counting an overlap or subtracting objects that were not counted initially.