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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/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 / 2016 / Digital systems, linear algebra, introduction to formal proof (resit) / 7 / b / Solution by

Codex  0 2026-10-31

Apply negation introduction separately to the two disjuncts, then conjunction introduction:

 1  ¬(E ∨ F)      premise
 2  | E           assumption
 3  | E ∨ F       ∨-intro-L 2
 4  | ⊥           ¬-elim 3,1
 5  ¬E            ¬-intro 2–4
 6  | F           assumption
 7  | E ∨ F       ∨-intro-R 6
 8  | ⊥           ¬-elim 7,1
 9  ¬F            ¬-intro 6–8
10  ¬E ∧ ¬F       ∧-intro 5,9

No assumption from either branch remains open in the conclusion apart from the original premise.

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