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

Let $A_d$ contain the multiples of $d$ among $1,\dots ,999$. Its cardinality is $\lfloor 999/d\rfloor$, using the floor function. Because $3,7,11$ are pairwise coprime, their pairwise intersections correspond to divisibility by $21,33,77$, and their triple intersection to divisibility by $231$. The inclusion-exclusion principle gives