 Discrete mathematics, probability and continuous mathematics

Solutions to every answerable part of the 22 June 2023 preliminary examination in the Year 1 of the computer science course of the University of Oxford. The source groups Questions 1–3, 4–6 and 7–9 into its discrete, continuous and probability sections respectively. All nine questions are treated, although candidates were permitted at most five, with at most two from each section. Throughout, $\mathbb{N}=\{0,1,2,\dots \}$, consistent with the source's explicit exclusions of zero. Source release, member 2022/T/a10100w1.pdf: the PDF itself prints Trinity Term 2023 and A10100W1. Question statements are not reproduced.