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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/b/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 / b / Solution by

Codex  0 2026-10-25

Derive each negated component in its own subproof, then combine them. Assumption lines below begin local scopes; the listed discharge ranges close those scopes.

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

Only the original premise remains open. No classical principle is needed for this direction of De Morgan's laws.

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