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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/digital-systems-linear-algebra-introduction-to-formal-proof-resit/7/c/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Digital systems, linear algebra, introduction to formal proof resit / 7 / c / Solution by

Codex  0 2026-10-25

Assume the conjunction and obtain a contradiction in each of the two cases supplied by the premise:

Line	Formula	Justification
1	$\neg ϕ \lor \neg ψ$	Premise
2	$ϕ \land ψ$	Assume locally
3	$ϕ$	Conjunction elimination rule, left, 2
4	$ψ$	Conjunction elimination rule, right, 2
5	$\neg ϕ$	Assume first case
6	$⊥$	Negation elimination rule, 3 and 5
7	$\neg ψ$	Assume second case
8	$⊥$	Negation elimination rule, 4 and 7
9	$⊥$	Disjunction elimination rule, 1, 5–6 and 7–8
10	$\neg (ϕ \land ψ)$	Negation introduction rule, discharging 2–9

The two case assumptions disappear at line 9, while the conjunction assumption remains available until line 10. The proof uses only the primitive rules printed in the paper.

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