 Solution

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/e/ii/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 / e / ii / Solution by

Codex  0 2026-10-31

Now derive the needed

D

E

inside its respective subproof:

 1  A → D          premise
 2  ¬A → E         premise
 3  (A ∧ D) → B    premise
 4  (¬A ∧ E) → B   premise
 5  A ∨ ¬A         excluded middle
 6  | A            assumption
 7  | D            →-elim 1,6
 8  | A ∧ D        ∧-intro 6,7
 9  | B            →-elim 3,8
10  | ¬A           assumption
11  | E            →-elim 2,10
12  | ¬A ∧ E       ∧-intro 10,11
13  | B            →-elim 4,12
14  B              ∨-elim 5,6–9,10–13

Implication elimination supplies the branch-specific premise before conjunction introduction packages it for the final implication.

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