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How would you prove the following by disjunction elimination?

Premises: A ∨ B , A ∨ C

Conclusion: A ∨ (B ∧ C)

1 Answers1

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  1. Premise: A v B
  2. Case 1: A
  3. Then, we can just get A v (B ∧ C) and it's works.
  4. Case 2: B (where A is false)
  5. Premise: A v C
  6. since NOT A, we get C (because A v C is true)
  7. so, A v (B ∧ C)